tag:blogger.com,1999:blog-90345721275352242902024-03-12T21:43:49.000-07:00Research LOVEs Dreamskysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-9034572127535224290.post-82320431383504828392016-01-09T05:17:00.002-08:002016-01-09T05:17:54.484-08:00Chapter 2 Core Element of a Program – Introduction with Python<h1 style="margin-left: 0cm; mso-text-indent-alt: 0cm; text-indent: 0cm;">
<br /></h1>
<div class="MsoNormal">
At the end of previous chapter we have learn how to choose
among variety in programming languages. And we have preferred to use Python in
this course. But keep in mind, this course is not about Python. We use python
as a tools to present concept that related with computational problem solving
and thinking. There are many excellent online resources in the internet, that describing
almost every aspect of the language. Python features that we don't need for
that purpose are not presented at all.</div>
<div class="MsoNormal" style="margin-left: 1.0cm;">
“<i>Since its introduction by Guido von Rossum in 1990, Python has
undergone many changes. For the first decade of its life, Python was a little
known and little used language. That changes with the arrival of Python 2.0 in
2000. In addition to incorporating a number of important improvements to the
language its self, it marked a shift in evolutionary path of the language. A
large number of people began developing libraries that interfaced seamlessly
with Python, and continuing support and development of the python ecosystem
became a community based activity. Python 3.0 was released at the end of 2008.
This version of Python cleaned up many of the inconsistencies in the design of
the various releases of Python 2 (often referred as Python 2.x). However, it
was not backward compatible. That means that most programs written for earlier
version of Python could not be run using implementation of Python 3.0.</i> </div>
<div class="MsoNormal" style="margin-left: 1.0cm;">
<i>The backward incompatibility presents a problem for this course. In our
view, Python 3.0 is clearly superior to Python 2.x. However, at the time of
this writing, some important Python libraries still do not work with Python 3.
We will, therefore, use Python 2.7 (into which many of the most important
features of Python 3 have been "back ported") throughout this course.</i>“
- <w:sdt citation="t" id="264004270"><!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>CITATION Gut13 \l 1033 <span
style='mso-element:field-separator'></span><![endif]-->(Guttag, 2013)<!--[if supportFields]><span style='mso-element:
field-end'></span><![endif]--></w:sdt></div>
<div class="MsoNormal">
<b>The Basic Element of a
Program <o:p></o:p></b></div>
<div class="MsoNormal">
A python program, sometimes called a <b>script</b>, is a sequence of definitions and commands are executed by
the Python interpreter in something called the shell. Typically, a new shell is
created whenever execution of a program begins. In most cases, a window is
associated with the shell. - <w:sdt citation="t" id="264004273"><!--[if supportFields]><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>CITATION Gut13 \l
1033 <span style='mso-element:field-separator'></span><![endif]-->(Guttag, 2013)<!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--></w:sdt>. To have a bettter
understanding about a computer program, we have to look the basic element that
build a every good program. And here it is:</div>
<div class="MsoNormal">
<br /></div>
<h2>
<!--[if !supportLists]-->2.1<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Statement/command</h2>
<div class="MsoNormal">
Sometimes computer didn’t have to make an operation and just
do a certain task, like printing something out, or take an input from an input
device or from another program. A command is an instruction given by a user
telling a computer to execute something, such a run a single program or a group
of linked programs. Commands are generally issued by typing them in at the
command line (i.e., the all-text display mode) and then pressing the ENTER key,<w:sdt citation="t" id="208413358"><!--[if supportFields]><span style='mso-element:
field-begin'></span> CITATION Com04 \l 1033 <span style='mso-element:field-separator'></span><![endif]--> (Command
Definition, 2004)<!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--></w:sdt></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<h2>
<!--[if !supportLists]-->2.2<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Object</h2>
<div class="MsoNormal">
Object are the core things that Python programs manipulate.
Every object has a type that defines the kinds of things that programs can do
with objects of that type. <w:sdt citation="t" id="154610829"><!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>CITATION Gut13 \l 1033 <span
style='mso-element:field-separator'></span><![endif]-->(Guttag, 2013)<!--[if supportFields]><span style='mso-element:
field-end'></span><![endif]--></w:sdt>. Object have two characteristic, there
are states and behavior. For Example, aircraft can have state (position,
altitude, angle, engine thrust) and behavior (rolling, pull up, climbing, full
throttle). <w:sdt citation="t" id="154610830"><!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>CITATION Wal96 \l 1033 <span
style='mso-element:field-separator'></span><![endif]-->(Walrath, 1996)<!--[if supportFields]><span style='mso-element:
field-end'></span><![endif]--></w:sdt><w:sdt citation="t" id="154610831"><!--[if supportFields]><span
style='mso-element:field-begin'></span> CITATION Mar96 \l 1033 <span
style='mso-element:field-separator'></span><![endif]--> (Walrath, What Is an Object?,
1996)<!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--></w:sdt></div>
<div class="MsoNormal">
As what we learn before that every object has a type. These
kind of types can be classified by two kind of object type, that are either scalar
or non-scalar. Scalar objects are indivisible, cause of each only have a single
value. Countrary with that, non-scalar objects that are divisible. For example,
17 as INT is a scalar object. In the other hand 17 as STR is a non-scalar
object because of it consist of 1 (STR) and 7 (STR). These are some example of
object types:</div>
<h3>
<!--[if !supportLists]-->2.2.1<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Object scalar</h3>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]--><b>int</b> is
used to represent integers. Literals of type <span style="font-family: "Kartika","serif";">int</span>
are written in the obvious way, e.g. 3 or 10002 or -4.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]--><b>float</b>
is used to represent real numbers. Literals of Type float are also written in
the obvious way, e.g. 3.0 or 3.37 or -27.72. (It is rarely used, but it is also
possible to write literals of type float using scientific notation. For
example, the literal 1.6E3 stands for 1.6×10<sup>3</sup>,i.e., it is the same
as 1600) You might wonder why this type is not called real. Within the
computer, values of type float are store in the computer as <i>Floating Point Numbers</i> <span style="font-family: Wingdings; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">à</span>
this representation, which is used by all modern programming languages, has
many advantages. However, under some situation it causes floating point
arithmatic to behave in ways that are slightly different from real arithmatic.
We will disscus this in Chapter 3.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]--><b>bool </b>is
used to represent the Boolean value True and False.</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]--><b>none</b>
is a type with a single value. We will say more about this when we get to
variables.</div>
<h3>
<!--[if !supportLists]-->2.2.2<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Object non scalar</h3>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 18.0pt; mso-add-space: auto; mso-list: l2 level1 lfo3; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]-->Str </div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 18.0pt; mso-add-space: auto; mso-list: l2 level1 lfo3; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]-->Array</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<h2>
<!--[if !supportLists]-->2.3<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Operator</h2>
<div class="MsoNormal">
Operator is about what computer will do with the object. As
we see in Chapter 1, each instruction build from operand and operator. So, all
programming languages will provide a set of operator, which generate generally
same behavior. Based on the expression, these operators can divide into 4 kind
of types:</div>
<h3>
<!--[if !supportLists]-->2.3.1<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Aritmatic operator</h3>
<div class="MsoNormal">
This type of operator is use when we want to calculate
something. When we use aritmatic operator, we will get aritmatic expression</div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="background: #F7F7F7; border-collapse: collapse; border: none; mso-border-alt: solid #D6D6D6 .75pt; mso-padding-alt: 0cm 0cm 0cm 0cm; mso-table-layout-alt: fixed; mso-yfti-tbllook: 1184; width: 560px;">
<tbody>
<tr>
<td style="background: #EEEEEE; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" width="65">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Operator<o:p></o:p></span></b></div>
</td>
<td style="background: #EEEEEE; border-left: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Description<o:p></o:p></span></b></div>
</td>
<td style="background: #EEEEEE; border-left: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Example<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" valign="top" width="65">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">+<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" valign="top" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Addition
- Adds values on either side of the operator<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" valign="top" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">a + b
will give 30<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" valign="top" width="65">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">-<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" valign="top" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Subtraction
- Subtracts right hand operand from left hand operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" valign="top" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">a - b
will give -10<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" valign="top" width="65">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">*<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" valign="top" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Multiplication
- Multiplies values on either side of the operator<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" valign="top" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">a * b
will give 200<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" valign="top" width="65">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">/<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" valign="top" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Division
- Divides left hand operand by right hand operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" valign="top" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">b / a
will give 2<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" valign="top" width="65">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">%<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" valign="top" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Modulus -
Divides left hand operand by right hand operand and returns remainder<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" valign="top" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">b % a
will give 0<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" valign="top" width="65">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">**<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" valign="top" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Exponent
- Performs exponential (power) calculation on operators<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" valign="top" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">a**b will
give 10 to the power 20<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 48.75pt;" valign="top" width="65">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">//<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 10.0cm;" valign="top" width="378">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Floor
Division - The division of operands where the result is the quotient in which
the digits after the decimal point are removed.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 87.75pt;" valign="top" width="117">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">9//2 is
equal to 4<o:p></o:p></span></div>
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">and<o:p></o:p></span></div>
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";"> 9.0//2.0 is equal to 4.0<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]-->2.3.2<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Comparison operator</h3>
<div class="MsoNormal">
When we want to know about something and how it’s value or
property, we usually compare it with an object that has a known value or
object. It is like when we use ‘meter (m)’ as a base unit to evaluate length of
a box. </div>
<div class="MsoNormal">
* Remember to only compare two object that has the same
type.</div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="background: #F7F7F7; border-collapse: collapse; border: none; mso-border-alt: solid #D6D6D6 .75pt; mso-padding-alt: 0cm 0cm 0cm 0cm; mso-yfti-tbllook: 1184; width: 560px;">
<tbody>
<tr>
<td style="background: #EEEEEE; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 38.25pt;" width="51">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Operator<o:p></o:p></span></b></div>
</td>
<td style="background: #EEEEEE; border-left: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 180.75pt;" width="241">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Description<o:p></o:p></span></b></div>
</td>
<td style="background: #EEEEEE; border-left: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Example<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">==<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Checks if
the value of two operands are equal or not, if yes then condition becomes
true.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">(a == b)
is not true.<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">!=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Checks if
the value of two operands are equal or not, if values are not equal then
condition becomes true.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">(a != b)
is true.<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";"><><o:p> </o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Checks if
the value of two operands are equal or not, if values are not equal then
condition becomes true.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">(a
<> b) is true. This is similar to != operator.<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">><o:p> </o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Checks if
the value of left operand is greater than the value of right operand, if yes
then condition becomes true.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">(a >
b) is not true.<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";"><<o:p> </o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Checks if
the value of left operand is less than the value of right operand, if yes
then condition becomes true.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">(a <
b) is true.<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">>=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Checks if
the value of left operand is greater than or equal to the value of right
operand, if yes then condition becomes true.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">(a >=
b) is not true.<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";"><=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Checks if
the value of left operand is less than or equal to the value of right
operand, if yes then condition becomes true.<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">(a <=
b) is true.<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]-->2.3.3<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Logic operator</h3>
<div class="MsoNormal">
We use logic operator when we want computer to think like us.
There only two main kind of logic operator that are:</div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 21.3pt; mso-add-space: auto; mso-list: l3 level1 lfo4; text-indent: -21.3pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]-->AND operator</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 21.3pt; mso-add-space: auto; mso-list: l3 level1 lfo4; text-indent: -21.3pt;">
<!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><!--[endif]-->OR operator</div>
<div class="MsoNormal">
With this operator we can tell computer to use all the
expression that allowed and provide us a conclusion.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]-->2.3.4<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Assignment operator</h3>
<div class="MsoNormal">
After make a conclusion, usually, we want to assign a
computer object to do or get something. For this, we will use assignment
operator as following:</div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="background: #F7F7F7; border-collapse: collapse; border: none; mso-border-alt: solid #D6D6D6 .75pt; mso-padding-alt: 0cm 0cm 0cm 0cm; mso-yfti-tbllook: 1184; width: 560px;">
<tbody>
<tr>
<td style="background: #EEEEEE; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 38.25pt;" width="51">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Operator<o:p></o:p></span></b></div>
</td>
<td style="background: #EEEEEE; border-left: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt; width: 180.75pt;" width="241">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Description<o:p></o:p></span></b></div>
</td>
<td style="background: #EEEEEE; border-left: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Example<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Simple
assignment operator, Assigns values from right side operands to left side
operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c = a + b
will assigne value of a + b into c<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">+=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Add AND
assignment operator, It adds right operand to the left operand and assign the
result to left operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c += a is
equivalent to c = c + a<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">-=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Subtract
AND assignment operator, It subtracts right operand from the left operand and
assign the result to left operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c -= a is
equivalent to c = c - a<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">*=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Multiply
AND assignment operator, It multiplies right operand with the left operand
and assign the result to left operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c *= a is
equivalent to c = c * a<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">/=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Divide
AND assignment operator, It divides left operand with the right operand and
assign the result to left operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c /= a is
equivalent to c = c / a<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">%=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Modulus
AND assignment operator, It takes modulus using two operands and assign the
result to left operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c %= a is
equivalent to c = c % a<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">**=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Exponent
AND assignment operator, Performs exponential (power) calculation on
operators and assign value to the left operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c **= a
is equivalent to c = c ** a<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #D6D6D6 1.0pt; mso-border-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">//=<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">Floor
Dividion and assigns a value, Performs floor division on operators and assign
value to the left operand<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #D6D6D6 1.0pt; border-left: none; border-right: solid #D6D6D6 1.0pt; border-top: none; mso-border-alt: solid #D6D6D6 .75pt; mso-border-left-alt: solid #D6D6D6 .75pt; mso-border-top-alt: solid #D6D6D6 .75pt; padding: 3.75pt 3.75pt 3.75pt 3.75pt;">
<div align="left" class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Helvetica","sans-serif"; font-size: 9.0pt; mso-fareast-font-family: "Times New Roman";">c //= a
is equivalent to c = c // a<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<h2>
<!--[if !supportLists]-->2.4<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Expression</h2>
<div class="MsoNormal">
In simple way expression is a type of instruction that we
make when we combine object (operand) with operator, which denote an object of
a type. That why, every expression consists of at least one operand and can
have one or more operators. For example, in the C language x+5 is an
expression, as is the character string "MONKEYS." From expression we
can get instruction (See section 1.2.1). An instruction can build by a single
expression or from many of it. Example, when we use looping we need to
expression to compare each other. </div>
<div class="MsoNormal">
In programming, an expression is any legal combination of operand
(object) and operator that have a value. Each programming language and
application has its own rules for what is legal and illegal. I suggest to see
again section 1.6.</div>
<div class="MsoNormal">
Expressions are often classified by the type of operand or
object that they represent. For example:</div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l4 level1 lfo5; text-indent: -18.0pt;">
</div>
<ul>
<li><span style="font-family: Wingdings; text-indent: -18pt;">§<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><span style="text-indent: -18pt;">Boolean expressions: Evaluate to either TRUE or
FALSE</span></li>
<li><span style="font-family: Wingdings; text-indent: -18pt;">§<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><span style="text-indent: -18pt;">Integer expressions: Evaluate to whole numbers,
like 3 or 100</span></li>
<li><span style="font-family: Wingdings; text-indent: -18pt;">§<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><span style="text-indent: -18pt;">Floating-point expressions: Evaluate to real
numbers, like 3.141 or -0.005</span></li>
<li><span style="font-family: Wingdings; text-indent: -18pt;">§<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal;">
</span></span><span style="text-indent: -18pt;">String expressions: Evaluate to character
strings</span></li>
</ul>
<!--[if !supportLists]--><br />
<div class="MsoNormal">
<br /></div>
<h2>
<!--[if !supportLists]-->2.5<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Variable</h2>
<div class="MsoNormal">
Every program language has a different meaning for variable.
In Python a variable just a name for an object. We use an assignment operator
to combine and object with variable. An object can have one or more than one
name that associated with it. Example:</div>
<div class="MsoNormal" style="margin-left: 2.0cm;">
<i>Pi = 3.14159<o:p></o:p></i></div>
<div class="MsoNormal" style="margin-left: 2.0cm;">
<i>Phi = 3.14159</i></div>
<div class="MsoNormal">
Those two expression is an example of naming floating object
3.14159 with variable <i>Pi</i> and <i>Phi</i>. </div>
<div class="MsoNormal">
In Python, variable names can contain letter, digits &
special character _. Python variable name are also case-sensitive. There are a
small number of reserved keywords in python that have built-in meaning and
cannot be used as variable names. Those word are usually have been used as
command or statement. Example in Python 2.7 are <i>and</i> <i>class</i>, <i>del</i>, <i>pass</i>,
<i>print</i>, <i>while</i>, etc. <w:sdt citation="t" id="264004268"><!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>CITATION Gut13 \l 1033 <span
style='mso-element:field-separator'></span><![endif]-->(Guttag, 2013)<!--[if supportFields]><span style='mso-element:
field-end'></span><![endif]--></w:sdt></div>
<div class="MsoNormal">
<br /></div>
<h2>
<!--[if !supportLists]-->2.6<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Comment</h2>
<div class="MsoNormal">
Purpose of a comment is to make a program easy to read (by
programmer). Comment will helps programmer to produce a well form program. Not
to explain the language or the semantics but to explain the thinking behind the
program or to explain the algorithm. So we suggest to assume the reader
understand the language.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<h2>
<!--[if !supportLists]-->2.7<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Branching program</h2>
<div class="MsoNormal">
The kind of computation we have been looking at this far are
called straight-line program. They execute one statement after another in the
order in which they appear, and stop when they run out of statements. These
kind of programs aren't very interesting. In fact, they are downright boring. <w:sdt citation="t" id="264004269"><!--[if supportFields]><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>CITATION Gut13 \l
1033 <span style='mso-element:field-separator'></span><![endif]-->(Guttag, 2013)<!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--></w:sdt></div>
<div class="MsoNormal">
There are three way to branching a program.</div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]-->2.7.1<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Conditional (If …)</h3>
<div class="MsoNormal">
The simplest statement to branching a program is to use a
conditional. A conditional statement
usually has three part:</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrRf8N5QGElMZGdoQPbecZt_Gdeck6HqIhfIWt8cQqFIB4oYUJdtiAU6PdjwYj7tLHqd8kotlJqu3Q9LWcs5N4O_JgU17Ied-fRPEJHV-oHkMJcMju9_k1alhkop4ImYFryt7Afl5d5DHy/s1600/Figure+2.1+-+Conditional+Branching+Program.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="267" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrRf8N5QGElMZGdoQPbecZt_Gdeck6HqIhfIWt8cQqFIB4oYUJdtiAU6PdjwYj7tLHqd8kotlJqu3Q9LWcs5N4O_JgU17Ied-fRPEJHV-oHkMJcMju9_k1alhkop4ImYFryt7Afl5d5DHy/s320/Figure+2.1+-+Conditional+Branching+Program.png" width="320" /></a></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /><!--[endif]--></div>
<div align="center" class="MsoNormal" style="text-align: center;">
Figure 2.1 - Conditional
Branching Program</div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 1.0cm; mso-add-space: auto; mso-list: l1 level8 lfo1; text-indent: -14.15pt;">
<!--[if !supportLists]-->a.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]--><span style="color: #0070c0;">a test</span>, i.e., an expression that evaluates to
eather true or false;</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0cm; mso-add-space: auto; mso-list: l1 level8 lfo1; text-indent: -14.15pt;">
<!--[if !supportLists]-->b.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]--><span style="color: #00b050;">a block of code </span>that is executed if the test
evaluates to<span style="color: #00b050;"> True</span>; and</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.0cm; mso-add-space: auto; mso-list: l1 level8 lfo1; text-indent: -14.15pt;">
<!--[if !supportLists]-->c.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]--><span style="color: red;">an optional block of code </span>that is executed if the test
evaluates to<span style="color: red;"> false</span>.</div>
<div class="MsoNormal">
Becarefull!!! In python indentation is a semantically
meaningfull. </div>
<h3>
<!--[if !supportLists]-->2.7.2<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Looping or iteration</h3>
<div class="MsoNormal">
A generic iteration mechanism is depict in figure .... Like
a conditional statement, it begins with a test. If the test evaluate to true,
the program execute the loop body once, and then goes back to reevaluate the
test. this process repeat until the test evaluates to False, after which
control passes the code following the iteration statement.</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioxPCFcyD_SBi98xvpSLMW2dG9UNDkTTbLNDuMuMr0maW7qWhbmQx_BIYC9NPJW7dCvCaDAhL2omL0kCnroDjcM6ejDvqbUVmZnFBaLFWSmc1W6Z9XsxV51WBfGfQWeHPA4xLc_E9e9Td2/s1600/Figure+2.2+-+Iteration+Branching+Program.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="267" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioxPCFcyD_SBi98xvpSLMW2dG9UNDkTTbLNDuMuMr0maW7qWhbmQx_BIYC9NPJW7dCvCaDAhL2omL0kCnroDjcM6ejDvqbUVmZnFBaLFWSmc1W6Z9XsxV51WBfGfQWeHPA4xLc_E9e9Td2/s320/Figure+2.2+-+Iteration+Branching+Program.png" width="320" /></a></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /><!--[endif]--></div>
<div align="center" class="MsoNormal" style="text-align: center;">
Figure 2.2 -
Iteration Branching Program</div>
<div class="MsoNormal">
There are two type of statement in iteration, that are:</div>
<h4>
<!--[if !supportLists]-->2.7.2.1<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Countable Looping (For …)</h4>
<div class="MsoNormal">
Executes a piece of script multiple times and abbreviates
the code that manages the loop variable. <w:sdt citation="t" id="273626708"><!--[if supportFields]><span
style='mso-element:field-begin'></span><span style='mso-spacerun:yes'> </span>CITATION
tut16 \l 1033 <span style='mso-element:field-separator'></span><![endif]-->(tutorialspoint.com)<!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--></w:sdt> The number of repetition
determined by the program or the user.
The loop "counts" the number of times the body will be
executed. This loop is a good choice
when the number of repetitions is known, or can be supplied by the user. <w:sdt citation="t" id="273626707"><!--[if supportFields]><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>CITATION mat16 \l
1033 <span style='mso-element:field-separator'></span><![endif]-->(mathbits.com)<!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--></w:sdt></div>
<div class="MsoNormal">
<br /></div>
<h4>
<!--[if !supportLists]-->2.7.2.2<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Conditional Looping (While …)</h4>
<div class="MsoNormal">
Repeats a statement or group of statements while a given
condition is TRUE. It tests the condition before executing the loop body. <w:sdt citation="t" id="273626709"><!--[if supportFields]><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>CITATION tut16 \l
1033 <span style='mso-element:field-separator'></span><![endif]-->(tutorialspoint.com)<!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--></w:sdt> If the
"condition" is FALSE at the beginning of the loop, the loop is never
executed. The "condition" may
be determined by the user at the keyboard.
The "condition" may be a numeric or an alphanumeric entry.<w:sdt citation="t" id="273626706"><!--[if supportFields]><span style='mso-element:
field-begin'></span> CITATION mat16 \l 1033 <span style='mso-element:field-separator'></span><![endif]--> (mathbits.com)<!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--></w:sdt> This is a good, when we focus on the “condition”,
and we don’t care about the number of repetition.</div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]-->2.7.3<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Steps Jumping </h3>
<h4>
<!--[if !supportLists]-->2.7.3.1<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->(Jump … / Go To…)</h4>
<div class="MsoNormal">
This is the simplest statement to jumping from one sequence of
statement to another.</div>
<h4>
<!--[if !supportLists]-->2.7.3.2<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Function /
subroutine</h4>
<div class="MsoNormal">
We will discusses this in a chapter, later.</div>
<div class="MsoNormal">
<br /></div>
<h1 style="text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-size: 12.0pt;">Bibliography</span><w:sdtpr></w:sdtpr></h1>
<div class="MsoNormal">
<br /></div>
<div class="MsoBibliography" style="text-indent: 1.0cm;">
<!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>BIBLIOGRAPHY <span style='mso-element:field-separator'></span><![endif]--><i>Command Definition</i>. (2004, June 15). Retrieved August 27, 2014, from www.linfo.org:
http://www.linfo.org/command.html<o:p></o:p><w:sdtpr></w:sdtpr></div>
<div class="MsoBibliography" style="text-indent: 1.0cm;">
<i>Expression</i>. (n.d.). Retrieved
12 04, 2015, from www.webopedia.com:
http://www.webopedia.com/TERM/E/expression.html<o:p></o:p></div>
<div class="MsoBibliography" style="text-indent: 1.0cm;">
Guttag, J. V. (2013). <i>Introduction to Computation and Programming
Using Python</i> (spring 2013 ed.). Cambridge, Massachusetts: The MIT Press.<o:p></o:p></div>
<div class="MsoBibliography" style="text-indent: 1.0cm;">
Mathbits.com. (n.d.). <i>Which LOOP should I use????</i> Retrieved
January 9, 2016, from http://mathbits.com:
http://mathbits.com/MathBits/CompSci/looping/whichloop.htm<o:p></o:p></div>
<div class="MsoBibliography" style="text-indent: 1.0cm;">
Tutorialspoint.com. (n.d.). <i>Python Loops</i>. Retrieved January 9,
2016, from http://www.tutorialspoint.com:
http://www.tutorialspoint.com/python/python_loops.htm<o:p></o:p></div>
<div class="MsoBibliography" style="text-indent: 1.0cm;">
Walrath, M. C. (1996). The Java Tutorial - Object-Oriented Programming
for the Internet. Addison-Wesley Pub.<o:p></o:p></div>
<w:sdt docparttype="Bibliographies" docpartunique="t" id="273626710" sdtdocpart="t">
<w:sdt bibliography="t" id="111145805">
</w:sdt></w:sdt><br />
<div class="MsoBibliography">
<span style="mso-no-proof: yes;">Walrath, M. C. (1996,
August). <i>What Is an Object?</i> Retrieved December 2014, from
http://journals.ecs.soton.ac.uk/:
http://journals.ecs.soton.ac.uk/java/tutorial/java/objects/object.html</span><!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--></div>
skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-41728470193938748792015-05-28T00:33:00.002-07:002015-05-28T00:35:31.305-07:00Turunan (SMA XI)<div align="center" class="MsoNormal" style="text-align: center;">
<b><u><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;"><a href="http://downloads.ziddu.com/download/24539945/Turunan---Sky-Note-.pdf.html">Download pdf-nya di sini</a></span></u></b></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b><u><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;"><br /></span></u></b></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b><u><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;">Turunan<o:p></o:p></span></u></b></div>
<div class="MsoListParagraphCxSpFirst" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->1.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Definisi</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
Archimedes
(287-212), Kepler (1571-1630), Galileo (1564-1642), Newton (1642-1727) dan
Leibniz (1646-1716).</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
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<v:formulas>
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<v:f eqn="prod @3 21600 pixelHeight">
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</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1087" style="height: 110.25pt; mso-wrap-style: square; visibility: visible; width: 162pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
Turunan fungsi
f(x) adalah laju perubahan fungsi bila saat nilai domainnya mendekati 0.</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>df</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
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mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
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normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
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</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->2.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]--><v:rect filled="f" id="_x0000_s1028" style="height: 29.95pt; left: 0; margin-left: 218pt; margin-top: 14.05pt; position: absolute; text-align: left; width: 124.4pt; z-index: 3;">Notasi</v:rect></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSup><m:sSupPr><span
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</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>Notasi</m:r><m:r>
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mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>dy</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>dx</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>,
</m:r><m:r>dibaca</m:r><m:r> "</m:r></span></i><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:nor/></m:rPr>dy dx"</m:r><m:r><i
style='mso-bidi-font-style:normal'>, </i></m:r><m:r><i style='mso-bidi-font-style:
normal'>sering</i></m:r><m:r><i style='mso-bidi-font-style:normal'> </i></m:r><m:r><i
style='mso-bidi-font-style:normal'>dikenal</i></m:r><m:r><i
style='mso-bidi-font-style:normal'> </i></m:r><m:r><i style='mso-bidi-font-style:
normal'>dengan</i></m:r><m:r><i style='mso-bidi-font-style:normal'> </i></m:r><m:r><i
style='mso-bidi-font-style:normal'>notasi</i></m:r><m:r><i style='mso-bidi-font-style:
normal'> </i></m:r><m:r><i style='mso-bidi-font-style:normal'>Leibniz</i></m:r></span></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 27pt; width: 315pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image004.png">
</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->3.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Turunan
Fungsi Aljabar</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l4 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->a)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Turunan fungsi konstan y = f(x) = c </div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r>f</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>c</m:r><m:r>-</m:r><m:r>c</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=0</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 27.75pt; width: 228.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r><m:r>c</m:r><m:r>
</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>→</m:r><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=0</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 105pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image006.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l4 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->b)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Turunan fungsi f(x) = x<sup>n</sup> </div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>= </m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i></m:sup></m:sSup></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 219.75pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 9.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+</m:r><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>(</m:r><m:r>n</m:r><m:r>-</m:r><m:r>1)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>2!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+
…<span style='mso-spacerun:yes'> </span>+</m:r><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i></m:sup></m:sSup></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i></m:sup></m:sSup></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 27.75pt; width: 294.75pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--> <o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>(</m:r><m:r>n</m:r><m:r>-</m:r><m:r>1)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>2!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+
…<span style='mso-spacerun:yes'> </span>+</m:r><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i></m:sup></m:sSup></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 27.75pt; width: 256.5pt;" type="#_x0000_t75">
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<br /></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r><m:r>1+</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>(</m:r><m:r>n</m:r><m:r>-</m:r><m:r>1)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>2!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+
…<span style='mso-spacerun:yes'> </span>+</m:r><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>+</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 27.75pt; width: 258.75pt;" type="#_x0000_t75">
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<div class="MsoNormal" style="margin-left: 54.0pt; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>=</m:r></span></i><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:
115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0 </m:r></span></i></m:lim></m:limLow><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;mso-ansi-font-size:
9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:
115%;font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r><m:r>1+</m:r></span></i><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>(</m:r><m:r>n</m:r><m:r>-</m:r><m:r>1)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>2!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>+ …<span
style='mso-spacerun:yes'> </span>+</m:r><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>+</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:e></m:d></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 291.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image011.png">
</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoNormal" style="margin-left: 54.0pt; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:10.0pt;mso-ansi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:
115%;font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r><m:r>1+</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>n</m:r><m:r>(</m:r><m:r>n</m:r><m:r>-</m:r><m:r>1)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>2!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>0</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>+
</m:r><m:r><span style='color:#984806;mso-themecolor:accent6;mso-themeshade:
128'>… </span></m:r><m:r><span style='mso-spacerun:yes'> </span>+</m:r><m:r><span
style='color:#984806;mso-themecolor:accent6;mso-themeshade:128'>n</span></m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>1</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>0</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>n</m:r><m:r>-</m:r><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>+</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>0</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:e></m:d></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 24.75pt; width: 282pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image012.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 10.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:rect filled="f" id="_x0000_s1033" style="height: 21.9pt; left: 0; margin-left: 214pt; margin-top: 11.4pt; position: absolute; text-align: left; width: 143.4pt; z-index: -62;"><o:p></o:p></v:rect></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>
</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>→</m:r><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r><m:r>n</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 135pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image013.png">
</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l4 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->c)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Turunan fungsi y=g(x)±h(x) = u±v</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>dy</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>dx</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>±h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>±h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 27.75pt; width: 285.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image014.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 112.5pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r>g</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>±</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 27.75pt; width: 214.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image015.png">
</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:rect filled="f" id="_x0000_s1030" style="height: 23.6pt; left: 0; margin-left: 174.15pt; margin-top: 10.25pt; position: absolute; text-align: left; width: 228.2pt; z-index: -65;"></v:rect></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r><m:r>g</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)±h(</m:r><m:r>x</m:r><m:r>)
</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>→</m:r><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>(</m:r><m:r>x</m:r><m:r>)±</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 213.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image016.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l4 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->d)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Turunan fungsi y=g(x)·h(x) = u·v</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>dy</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>dx</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 225pt;" type="#_x0000_t75">
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<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 81.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";color:#984806;
mso-themecolor:accent6;mso-themeshade:128;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>+</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";color:#984806;
mso-themecolor:accent6;mso-themeshade:128;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 340.5pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 9.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 81.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r><m:r><span
style='color:#0070C0'>h</span></m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#0070C0;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#0070C0'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";color:#984806;
mso-themecolor:accent6;mso-themeshade:128;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#0070C0'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
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style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#0070C0'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>+</m:r></span></i><m:d><m:dPr><m:begChr
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mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
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normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif";color:#00B050'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
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mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#00B050'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
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italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
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mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
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mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
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style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#00B050'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#00B050;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#00B050'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 340.5pt;" type="#_x0000_t75">
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m:val="left"/></m:oMathParaPr><m:oMath><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r>g</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif";color:#0070C0'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#0070C0;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#0070C0'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:func><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>+</m:r><m:r><span
style='color:#00B050'>g</span></m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#00B050;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif";color:#00B050'><m:r>x</m:r></span></i></m:e></m:d><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
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11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 241.5pt;" type="#_x0000_t75">
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<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
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mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>→</m:r><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif";color:#0070C0'><m:r>+</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 13.5pt; width: 241.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image021.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 10.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>ata𝑢</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 23.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image022.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>y</m:r><m:r>=</m:r><m:r>u</m:r><m:r>∙</m:r><m:r>v</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>→</m:r><m:r>y</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r><m:r>u</m:r><m:r>'∙</m:r><m:r>v</m:r><m:r><span
style='color:#0070C0'>+</span></m:r><m:r>u</m:r><m:r>∙</m:r><m:r>v</m:r><m:r>'</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 141pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image023.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l4 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->e)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Turunan fungsi y=g(x)/h(x) = u/v</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>dy</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>dx</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:den></m:f></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:den></m:f></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 39pt; width: 191.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image024.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 112.5pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 24pt; width: 180pt;" type="#_x0000_t75">
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<div class="MsoListParagraphCxSpMiddle" style="margin-left: 81.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 112.5pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>-</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";color:#984806;
mso-themecolor:accent6;mso-themeshade:128;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>+</m:r></span></i><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";color:#984806;
mso-themecolor:accent6;mso-themeshade:128;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:#984806;mso-themecolor:accent6;mso-themeshade:128;font-style:
italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:den></m:f></m:e></m:func></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 24pt; width: 298.5pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 9.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 112.5pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;
mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
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color:#00B050'><m:r>x</m:r></span></i></m:e></m:d></m:num><m:den><i
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font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif";color:#00B050'><m:r>∙</m:r></span></i><m:f><m:fPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:9.0pt;mso-ansi-font-size:
9.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>-h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 24pt; width: 327pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 9.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:rect filled="f" id="_x0000_s1032" style="height: 82.95pt; left: 0; margin-left: 152.15pt; margin-top: 6.35pt; position: absolute; text-align: left; width: 275.55pt; z-index: -63;"></v:rect></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>f</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:den></m:f><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>→</m:r><m:r>f</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙h</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif";
color:#00B050'><m:r>-</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:115%;
font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><m:begChr
m:val="["/><m:endChr m:val="]"/><span style='font-size:10.0pt;
mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 27pt; width: 214.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image029.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 10.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<i>Atau
<o:p></o:p></i></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>y</m:r><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>u</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>v</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>→</m:r><m:r>y</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>u</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r><m:r>v</m:r><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="bi"/></m:rPr><b style='mso-bidi-font-weight:
normal'><span style='color:#00B050'>-</span></b></m:r><m:r>u</m:r><m:r>∙</m:r><m:r>v</m:r><m:r>'</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>v</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 27.75pt; width: 127.5pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--><i><o:p></o:p></i></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->4.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Turunan
Fungsi Trigonometri</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l2 level1 lfo3; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->a.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Turunan fungsi y = sin <i>x</i> </div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><m:sSup><m:sSupPr><span
style='font-size:9.0pt;mso-ansi-font-size:9.0pt;font-family:"Cambria Math","serif";
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<!--[if !supportLists]-->b.<span style="font-size: 7pt; font-stretch: normal;">
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<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
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mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:func><i
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<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
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style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
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font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:
115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0 </m:r></span></i></m:lim></m:limLow><i
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mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:num><m:den><i
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mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:f><m:fPr><span
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mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
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style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:den></m:f></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∙</m:r><m:r>sin</m:r></span></i><m:d><m:dPr><span
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mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;
mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:num><m:den><i
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mso-bidi-font-size:11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 37.5pt; width: 129pt;" type="#_x0000_t75">
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<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 63.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-size:9.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-family:
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mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:9.0pt;mso-bidi-font-size:
11.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r><m:r>+0</m:r></span></i></m:e></m:d></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 12pt; width: 68.25pt;" type="#_x0000_t75">
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<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
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<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l2 level1 lfo3; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->c.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Turunan fungsi fungsi trigonometri lain</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Ingat:</div>
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<!--[if !supportLists]-->5.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Turunan
Fungsi Komposisi f(x) = (g o h)(x)</div>
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<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
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mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
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style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
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style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
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style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
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</m:r><m:r>o</m:r><m:r> h</m:r></span></i></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>'</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
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<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
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style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
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style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#0070C0;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
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color:#00B050'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#00B050;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r><span
style='color:#0070C0'>g</span></m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
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<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
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style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#0070C0;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#00B050;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r><span
style='color:#0070C0'>g</span></m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#0070C0;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#984806;mso-themecolor:accent6;
mso-themeshade:128;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>-h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:den></m:f></m:e></m:func><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#984806;mso-themecolor:accent6;
mso-themeshade:128;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>-h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 31.5pt; width: 240.75pt;" type="#_x0000_t75">
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<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";color:#0070C0'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#0070C0;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#00B050;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>+∆h(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r><span
style='color:#0070C0'>g</span></m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#0070C0;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∆h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:den></m:f></m:e></m:func><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#984806;mso-themecolor:accent6;
mso-themeshade:128;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>-h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 30pt; width: 255.75pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 63.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 63.0pt; mso-add-space: auto; text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-family:"Cambria Math","serif"'><m:r>=</m:r></span></i><m:func><m:funcPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";color:#984806;
mso-themecolor:accent6;mso-themeshade:128'><m:r>∆h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>→0
</m:r></span></i></m:lim></m:limLow></m:fName><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";color:#0070C0'><m:r>g</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#0070C0;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#00B050;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>+∆h(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>-</m:r><m:r><span
style='color:#0070C0'>g</span></m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#0070C0;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#00B050'><m:r>h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:e></m:d></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>∆h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:den></m:f></m:e></m:func><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∙</m:r></span></i><m:limLow><m:limLowPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:limLowPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>lim</m:r></span></m:e><m:lim><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r><m:r>→0
</m:r></span></i></m:lim></m:limLow><m:f><m:fPr><span style='font-family:
"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
"Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>h</m:r></span></i><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:#984806;mso-themecolor:accent6;
mso-themeshade:128;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>x</m:r><m:r>+∆</m:r><m:r>x</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif";
color:#984806;mso-themecolor:accent6;mso-themeshade:128'><m:r>-h</m:r><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>∆</m:r><m:r>x</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 30pt; width: 292.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image057.png">
</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 63.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 36.0pt; text-align: justify;">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1045"
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</o:OLEObject>
</xml><![endif]--><o:p> </o:p></div>
<div class="MsoNormal" style="margin-left: 36.0pt; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpFirst" style="text-align: justify;">
<b>Atau</b> jika kita menggunakan
notasi Leibniz dan aturan rantai sebagai berikut:<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
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</v:imagedata></v:shape><v:shape id="_x0000_s1047" strokecolor="black [3213]" style="height: 32.45pt; left: 0; margin-left: 96.4pt; margin-top: 8.65pt; position: absolute; text-align: left; width: 147.7pt; z-index: 22;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image060.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1046"
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</xml><![endif]--><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1047"
DrawAspect="Content" ObjectID="_1494327602">
</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1048" strokecolor="black [3213]" stroked="t" style="height: 30.5pt; left: 0; margin-left: 183.75pt; margin-top: 52.3pt; position: absolute; text-align: left; width: 145.7pt; z-index: 23;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image061.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1048"
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</o:OLEObject>
</xml><![endif]--><o:p> </o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->6.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Turunan
Fungsi Logaritma</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l1 level1 lfo4; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->a.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Untuk fungsi f(x) = <sup>a</sup>log x </div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
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<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image062.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1050"
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1055"
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<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image064.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1057"
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</xml><![endif]--><v:shape id="_x0000_s1056" strokecolor="black [3213]" style="height: 40.25pt; left: 0; margin-left: 192pt; margin-top: 59.5pt; position: absolute; text-align: left; width: 109.8pt; z-index: 31;" type="#_x0000_t75">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1056"
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
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</xml><![endif]--><o:p> </o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1053"
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</o:OLEObject>
</xml><![endif]--><i><u>Misalkan</u></i> , maka saat , nilai . Dengan ini kita dapat merubah bentuk di atas
menjadi:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1061"
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<v:stroke dashstyle="dash">
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1066"
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</xml><![endif]--><v:shape id="_x0000_s1060" strokecolor="black [3213]" style="height: 78.3pt; left: 0; margin-left: 77.05pt; margin-top: 117.15pt; position: absolute; text-align: left; width: 170.35pt; z-index: 35;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image073.wmz">
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1060"
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1058"
DrawAspect="Content" ObjectID="_1494327617">
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</xml><![endif]--><o:p> </o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; tab-stops: 383.25pt; text-align: justify;">
</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:shape id="_x0000_s1062" strokecolor="black [3213]" style="height: 34.15pt; left: 0; margin-left: 77.05pt; margin-top: .8pt; position: absolute; text-align: left; width: 69.3pt; z-index: 37;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image075.wmz">
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1064"
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<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image077.wmz">
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1063"
DrawAspect="Content" ObjectID="_1494327620">
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</xml><![endif]--><o:p> </o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l1 level1 lfo4; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->b.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Untuk fungsi f(x) = ln x</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:shape id="_x0000_s1049" strokecolor="black [3213]" style="height: 30.45pt; left: 0; margin-left: 55.1pt; margin-top: 9.95pt; position: absolute; text-align: left; width: 73.85pt; z-index: 24;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image078.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1049"
DrawAspect="Content" ObjectID="_1494327621">
</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1065" strokecolor="black [3213]" stroked="t" style="height: 31.1pt; left: 0; margin-left: 205.75pt; margin-top: 48.9pt; position: absolute; text-align: left; width: 169.3pt; z-index: 40;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image079.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1065"
DrawAspect="Content" ObjectID="_1494327622">
</o:OLEObject>
</xml><![endif]--><o:p> </o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->7.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Turunan
Fungsi Eksponensial f(x) = e<sup>g(x)</sup></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
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<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image080.wmz">
</v:imagedata></v:shape><v:shape id="_x0000_s1068" strokecolor="black [3213]" style="height: 23.55pt; left: 0; margin-left: 40.85pt; margin-top: 30.7pt; position: absolute; text-align: left; width: 99.8pt; z-index: 43;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image081.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1067"
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</o:OLEObject>
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1068"
DrawAspect="Content" ObjectID="_1494327624">
</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1070" strokecolor="black [3213]" style="height: 19.6pt; left: 0; margin-left: 40.85pt; margin-top: 78.85pt; position: absolute; text-align: left; width: 81.85pt; z-index: 45;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image082.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1070"
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</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1069" strokecolor="black [3213]" style="height: 19.6pt; left: 0; margin-left: 40.85pt; margin-top: 54.9pt; position: absolute; text-align: left; width: 111.8pt; z-index: 44;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image083.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1069"
DrawAspect="Content" ObjectID="_1494327626">
</o:OLEObject>
</xml><![endif]--><o:p> </o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
Turunkan kedua
ruas dengan menggunakan turunan logaritma dan dalil rantai sehingga menjadi:</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<v:shape id="_x0000_s1071" strokecolor="black [3213]" style="height: 32.35pt; left: 0; margin-left: 40.85pt; margin-top: 1.75pt; position: absolute; text-align: left; width: 95.8pt; z-index: 46;" type="#_x0000_t75">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1073"
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1072"
DrawAspect="Content" ObjectID="_1494327629">
</o:OLEObject>
</xml><![endif]--><o:p> </o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->8.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Turunan
Fungsi Implisit f(x,y)=c</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
Fungsi implisit
f(x,y)=c, dimana y juga merupakan fungsi dari x.</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
Contoh:</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
Tentukan y’ dari
fungsi:</div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
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<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
<b><u>Cara</u></b>nya dengan menurunkan kedua
ruas terhadap x, seperti berikut: </div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: justify;">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1077"
DrawAspect="Content" ObjectID="_1494327632">
</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1079" strokecolor="black [3213]" style="height: 21.6pt; left: 0; margin-left: 127.65pt; margin-top: 146.75pt; position: absolute; text-align: left; width: 118.75pt; z-index: 54;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image090.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1079"
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</xml><![endif]--><v:shape id="_x0000_s1080" strokecolor="black [3213]" stroked="t" style="height: 39.3pt; left: 0; margin-left: 168.9pt; margin-top: 180.25pt; position: absolute; text-align: left; width: 89.8pt; z-index: 55;" type="#_x0000_t75">
<v:stroke dashstyle="dashDot">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image091.wmz">
</v:imagedata></v:stroke></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1080"
DrawAspect="Content" ObjectID="_1494327634">
</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1078" strokecolor="black [3213]" style="height: 17.65pt; left: 0; margin-left: 130.65pt; margin-top: 122.15pt; position: absolute; text-align: left; width: 113.75pt; z-index: 53;" type="#_x0000_t75">
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<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->9.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Turunan
Jenis Lebih Tinggi</div>
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<div class="MsoListParagraphCxSpMiddle" style="mso-list: l7 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->10.<span style="font-size: 7pt; font-stretch: normal;"> </span><!--[endif]-->Aplikasi
Turunan</div>
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<!--[if !supportLists]-->a.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Fungsi naik – Fungsi turun</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Untuk y=f(x), jika:</div>
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<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<b>f’(x) < 0</b>
atau f’(x) bernilai negatif, maka kurva y=f(x) akan <b>turun</b>.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<b>f’(x) = 0</b>,
maka kurva y=f(x) berada pada keadaan <b>stasioner.</b></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<b>f’(x) > 0</b>
atau f’(x) bernilai positif, maka kurva y=f(x) <b>akan naik</b>.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l6 level1 lfo6; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->b.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Nilai stationer (kritis) dari fungsi</div>
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Seperti yang dijelaskan pada bagian sebelumnya, nilai
stasioner dari sebuah fungsi akan diperoleh saat turunan pertama dari fungsi
tersebut sama dengan nol. Perhatikan grafik berikut</div>
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<v:shape id="Picture_x0020_5391" o:spid="_x0000_i1086" style="height: 150.75pt; mso-wrap-style: square; visibility: visible; width: 204.75pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image097.png">
</v:imagedata></v:shape></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Misalkan:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
f’(a)=f’(b)=f’(c)=0</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
maka nilai stationer dari fungsi tersebut adalah f(a),
f(b), dan f(c).</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l6 level1 lfo6; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->c.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Nilai maksimum – Nilai minimum</div>
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<br /></div>
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Masih berdasarkan gambar diatas, dengan menggunakan <u>analisis
nilai turunan pertama</u>:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l5 level1 lfo7; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->-<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Pada titik A, f’(x) berubah dari <i>positif menjadi negatif</i>, maka f(a) disebut
<b>nilai balik maksimum</b></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l5 level1 lfo7; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->-<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Pada titik B, f’(x) berubah dari <i>negatif-nol-negatif</i>, maka f(b) <b>disebut nilai belok horisontal</b></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l5 level1 lfo7; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->-<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Pada titik C, f’(x) berubah dari <i>negatif menjadi positif</i>, maka f(c)
disebut <b>nilai balik minimum</b></div>
<div class="MsoNormal" style="margin-left: 54.0pt; text-align: justify;">
Selain
menggunakan analisis turunan pertama, kita juga dapat menggunakan turunan kedua
untuk menentukan nilai balik/belok, seperti berikut:</div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 90.0pt; mso-add-space: auto; mso-list: l0 level1 lfo8; text-align: justify; text-indent: -36.0pt;">
<!--[if !supportLists]-->i.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->f(a) adalah nilai balik maksimum jika f’(a)=0
dan f’’(a)<0 a="" bernilai="" f="" negatif="" p=""><!--0--></0><br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 90.0pt; mso-add-space: auto; mso-list: l0 level1 lfo8; text-align: justify; text-indent: -36.0pt;">
<!--[if !supportLists]-->ii.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->f(c) adalah nilai balik minimum jika f’(c)=0 dan
f’’(c)>0 (f’’(c) bernilai positif)</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l6 level1 lfo6; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->d.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Menggambar bentuk grafik fungsi</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Langkah 1. Buat analisa awal sebagai berikut;</div>
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<i>1. Periksa daerah asal (domain) dan daerah hasil (range) fungsi untuk melihat
apakah ada daerah di bidang yang di kecualikan<o:p></o:p></i></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 117.0pt; mso-add-space: auto; text-align: justify; text-indent: -13.5pt;">
<i>2. Cari perpotongan dengan
sumbu-sumbu kordinat.<o:p></o:p></i></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 117.0pt; mso-add-space: auto; text-align: justify; text-indent: -13.5pt;">
<i>3. Gunakan turunan pertama untuk
mencari titik-titik stationer (kritis) dan untuk mengetahui tempat-tempat
grafik naik , turun, maupun berbalik secara horizontal. <o:p></o:p></i></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 117.0pt; mso-add-space: auto; text-align: justify; text-indent: -13.5pt;">
<i>4. Gunakan turunan kedua untuk
mengetahui tempat-tempat grafik cekung ke atas dan cekung ke bawah dan untuk
melokasikan ttik-titik balik.<o:p></o:p></i></div>
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Langkah 2 Gambarkan beberapa titik ( termasuk semua
titik kritis dan titik balik )</div>
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Langkah 3 Sketsa grafik</div>
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<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l6 level1 lfo6; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->e.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Menentukan Kecepatan dan percepatan</div>
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<i>Kecepatan</i> merupakan
turunan pertama dari sebuah fungsi terhadap waktu. <span style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-symbol-font-family: Wingdings;">à</span> <i>v = f’(t)<o:p></o:p></i></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<i>Percepatan</i>
merupakan turunan kedua dari sebuah fungsi terhadap waktu, atau merupakan
turunan pertama dari fungsi kecepatan terhadap waktu. <span style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-symbol-font-family: Wingdings;">à</span> <i>a = f’’(t) = v’(t)</i></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l6 level1 lfo6; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->f.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Menentukan elastisitas permintaan</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Elastisitas permintaaan(e<sub>D</sub>) adalah
perubahan relatif permintaan barang (b%) terhadap perubahan relatif harga
barang (a%). <span style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-symbol-font-family: Wingdings;">à</span> e<sub>D </sub>= ( b%/a%)</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Secara matematis:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Jika fungsi permintaan adalah Q<sub>Demand</sub>=f(Price),
maka</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
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<br /></div>
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<br /></div>
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<br /></div>
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<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto;">
Hal ini berlaku juga untuk elastisitas penawaran (e<sub>S</sub>) dan
elastisitas produksi (e<sub>P</sub>).</div>
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1085"
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<v:stroke joinstyle="miter">
<v:path gradientshapeok="t" o:connecttype="rect">
</v:path></v:stroke></v:shapetype></div>
<table cellpadding="0" cellspacing="0" style="width: 100%px;">
<tbody>
<tr>
<td><!--[endif]-->
<br />
<div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;">
e<sub>P</sub>
= Elastisitas Produksi</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;">
p = output</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;">
x = input</div>
</div>
<!--[if !mso]--></td>
</tr>
</tbody></table>
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<v:textbox>
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<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
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<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l6 level1 lfo6; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->g.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Analisis marginal</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Dalam ilmu ekonomi, istilah marginal diartikan sebagai
<i>laju perubahan</i> atau <i>turunan pertama</i> dari sebuah fungsi.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Misalkan:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
C(x) = total biaya untuk memproduksi x unit</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
R(x) = pendapatan total dari penjualan x unit</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
P(x) = Keuntungan total yang diperoleh dari penjualan
x unit produk</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Dari keterangan tersebut, maka dapat dihubungkan:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
P(x) = R(x) – C(x)</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
Sehingga:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
P’(x) = R’(x) – C’(x)</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
C’(x) = disebut <b>biaya
marginal</b></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
R’(x) = disebut <b>penerimaan
marginal</b></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">P’(x) = disebut <b>keuntungan
marginal<o:p></o:p></b></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l6 level1 lfo6; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]-->h.<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Aturan L’hopital </div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:shape id="_x0000_s1089" strokecolor="black [3213]" style="height: 19.6pt; left: 0; margin-left: 84.6pt; margin-top: 12.65pt; position: absolute; text-align: left; width: 80.85pt; z-index: 64;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image101.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1089"
DrawAspect="Content" ObjectID="_1494327643">
</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1090" strokecolor="black [3213]" style="height: 19.6pt; left: 0; margin-left: 205.1pt; margin-top: 10.4pt; position: absolute; text-align: left; width: 89.8pt; z-index: 65;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image102.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1090"
DrawAspect="Content" ObjectID="_1494327644">
</o:OLEObject>
</xml><![endif]--><span style="background: white; line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;">Jika:<br />
</span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;"> atau<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:shape id="_x0000_s1091" strokecolor="black [3213]" style="height: 34.3pt; left: 0; margin-left: 84.6pt; margin-top: 6.3pt; position: absolute; text-align: left; width: 50.9pt; z-index: 66;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image103.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1091"
DrawAspect="Content" ObjectID="_1494327645">
</o:OLEObject>
</xml><![endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;"> </span></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;"> memiliki nilai<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;">dan<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:shape id="_x0000_s1092" strokecolor="black [3213]" style="height: 19.6pt; left: 0; margin-left: 84.6pt; margin-top: 4.55pt; position: absolute; text-align: left; width: 48.9pt; z-index: 67;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image104.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1092"
DrawAspect="Content" ObjectID="_1494327647">
</o:OLEObject>
</xml><![endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;"> </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;">maka<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:shape id="_x0000_s1088" strokecolor="black [3213]" stroked="t" style="height: 37.05pt; left: 0; margin-left: 220pt; margin-top: 11.25pt; position: absolute; text-align: left; width: 108.1pt; z-index: 63;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image105.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1088"
DrawAspect="Content" ObjectID="_1494327648">
</o:OLEObject>
</xml><![endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;"> </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<br clear="ALL" />
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<span style="background: white; line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;">Penurunan:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<v:shape id="_x0000_s1093" strokecolor="black [3213]" style="height: 34.3pt; left: 0; margin-left: 54.6pt; margin-top: 9.55pt; position: absolute; text-align: left; width: 136.75pt; z-index: 68;" type="#_x0000_t75">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1093"
DrawAspect="Content" ObjectID="_1494327649">
</o:OLEObject>
</xml><![endif]--><v:shape id="_x0000_s1094" strokecolor="black [3213]" style="height: 65.65pt; left: 0; margin-left: 54.6pt; margin-top: 59.25pt; position: absolute; text-align: left; width: 230.55pt; z-index: 69;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\SkY\AppData\Local\Temp\msohtmlclip1\01\clip_image107.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_s1094"
DrawAspect="Content" ObjectID="_1494327650">
</o:OLEObject>
</xml><![endif]--><span style="background: white; line-height: 115%; mso-bidi-font-size: 12.0pt; mso-bidi-font-style: italic;"><o:p> </o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
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<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
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<br /></div>
<br />
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<br /></div>
<!--0--></div>
skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-84973734189209146372014-08-01T08:49:00.001-07:002014-08-01T08:49:37.367-07:00Chapter 1 Introduction to Computer Science & Programming<h1 align="center" style="margin-top: 0in; mso-list: l1 level1 lfo1; text-align: center;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%; text-indent: 0in;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%; text-indent: 0in;"> </span></h1>
<h2>
<!--[if !supportLists]-->1.1. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Declarative vs. Imperative</h2>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.1.1.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Declarative knowledge <o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Declarative knowledge is about “what we
want to achieve”. It’s composed by statements of fact [Declarative Programming].<span style="color: red;"> </span>Simple case, when we declare set of rules about what
outputs should result from which inputs. In other words, if we have A, then the
result must be B. An engine will apply these rules to inputs, and give us the
proper output. The focus is on <b>what</b>
the computer should do rather than how it should do it.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Example: <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l0 level5 lfo4; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">“A
good health care plan improves the quality of medical care while saving money”
- <i>declarative statement</i> -<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l0 level5 lfo4; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">“y
is the square root of x if and only if y*y = x”
- <i>declarative statement</i> -<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l0 level5 lfo4; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">SQL
- <i>declarative program</i> -<o:p></o:p></span></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.1.2.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Imperative knowledge<o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Imperative knowledge is about “<b>how to achieve</b> our goal or accomplish
something”. The focus is on what steps the computer should take rather than
what the computer will do (ex. C, C++, Java). Case in computer science, when we
specify a series of instructions that the computer executes in sequence (do
this, and then do that). We can think of it as recipe [Imperative Programming].
Example, when we specify instruction to find approximation of square root
(Heron of Alexandria method)<a href="file:///D:/Hobby/Bahan%20Kuliah%20MIT/Electrical%20Engineering%20and%20Computer%20Science/MIT%206.00SC%20Introduction%20to%20Computer%20Science%20and%20Programming,%20Spring%202011/Lecture%201/Sky%20Note/Ch1%20-%20Introduction%20to%20Computer%20Science%20(2014%2007%2021).docx#_ftn1" name="_ftnref1" title=""><span class="MsoFootnoteReference"><!--[if !supportFootnotes]--><span class="MsoFootnoteReference"><span style="font-size: 12pt; line-height: 115%;">[1]</span></span><!--[endif]--></span></a>:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 12.0pt; mso-list: l2 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Start
with a guess, <i>g</i><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If
<i>g</i>*<i>g</i>
is close enough to <i>x</i>, then <i>g</i> is a good approximation of the square
root of <i>x</i><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">3)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Otherwise,
create a new guess by averaging <i>g</i> and
<i>x</i>/<i>g</i>.
I.e., <i>g</i><sub>new</sub>= (<i>g</i><sub>old</sub>+ <i>x</i>/<i>g</i><sub>old</sub>)/2<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">4)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Using
this new guess, go back to step 2 <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">5)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Converged
(well done cook)<o:p></o:p></span></div>
<h2>
<!--[if !supportLists]-->1.2. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Program</h2>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">A computer program is a set of
instructions for a computer to perform a specific task. Programming is about
controlling the computer or <b>what</b>
computer should do. And to control the compiler we give it a program [Beginner
- Introduction to Programming]. To make a computer do anything, you have to
write a computer program. To write a computer program, you have to tell the
computer, step by step, exactly what you want it to do. The computer then
"executes" the program, following each step mechanically, <b>to accomplish the end goal</b> [What is a computer algorithm?].<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">When you are telling the computer <b>what</b> to do, you <b>also</b> have to choose <b>how</b>
it's going to do it. That's where computer algorithms come in [What is a computer algorithm?]. The algorithm
is the basic technique used to get the job done, or the detailed <b>sequence of steps</b> for carrying out some
process is called algorithm [What is the
differences between algorithm and program?].<span style="color: red;"> </span>Algorithm
composed by a finite set of instructions to solve a specific problem or class
of problems [Algorithm Analysis]. It is
about <b>how</b> to perform computation or <b>how</b> computer should perform a specific
task.<span style="color: red;"> <o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">So the computer program basically is the
<b>concrete expression of an algorithm</b>
in a particular programming language [Algorithm Analysis].
In other words a computer program is a specific implementation of an algorithm,
or set of algorithms designed to be used in conjunction with computer hardware
(and possibly other programs) to solve a problem whereas an algorithm does not
define the way it is to be implemented (though specific algorithms might by
their nature suggest specific implementations) [Algorithm
vs. Computer Program]. Ex, approximation program using the same Heron of
Alexandria algorithm written in C++ will differed than program written in Java.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">A computer <b>program</b> usually consist of:<o:p></o:p></span></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.2.1.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Instructions<o:p></o:p></span></h3>
<div class="MsoNormal" style="mso-list: none; text-align: justify; text-indent: .5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Instruction
means steps that can be executed. The instruction is the key element in the
computer, as it tells (orders) the processor which action should be performed.
The instructions which are to be executed are indicated in the source file and
the computer goes from one instruction to the next following the instructions
from top to bottom (as a file is read in sequence from top to bottom) [Programming Languages - Instructions]. <o:p></o:p></span></div>
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<div class="MsoNormal" style="text-align: center; text-indent: 0.5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Figure
1. Operator and operand(s); [Operator, 2012]<o:p></o:p></span></div>
<div class="MsoNormal" style="mso-list: none; text-indent: .5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">An
instruction is generally comprised of two elements:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .75in; margin-right: 0in; margin-top: 0in; mso-list: l5 level1 lfo8; tab-stops: 135.0pt; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">the operator : the action that the processor is to carry out <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 2.0in; mso-list: l5 level1 lfo8; tab-stops: .75in 135.0pt; text-indent: -1.5in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><img alt="*" height="13" src="file:///C:/Users/SkY/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="13" /><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">the operand(s) : one or more pieces of data on which the operation is performed<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: none;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">For
a better understanding, see Figure 1.<o:p></o:p></span></div>
<div class="MsoNormal" style="mso-list: none; text-align: justify; text-indent: .5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">At
the lowest level language, each instruction is a sequence of 0s and 1s that
describes a physical operation the computer is to perform (such as
"Add") and, depending on the particular instruction type, the
specification of special storage areas called registers that may contain data
to be used in carrying out the instruction, or the location in computer memory
of data. [Rouse, 2005]<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">In a computer's assembler language, each
language statement generally corresponds to <b>a single processor instruction</b>. In high-level languages, a language
statement generally results (after program compilation) in <b>multiple processor instructions</b> [Rouse,
2005]. In other words, a macro instruction is one that, during
processing by the assembler program, expands to become multiple instructions
(based on a previously coded macro definition) in high-level language [Rouse, 2005]. Alan Touring, the British
mathematician, says that with less than 7 ‘primitive instruction’ (single
processor instruction), each operate on 1 bit information, you can do anything.
It means you can build any kind of complex instruction with combine some of
main/single processor instruction. <o:p></o:p></span></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.2.2.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Control Structure / Flow of
Control / Control Flow <o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">When we run through a list of
instructions, normally, we go through them step by step. But what if that's not
the case? What if we are to press the red button when a tone is heard and the
green one when not? What if we are supposed to scream when a meltdown occurs
but shout when a fire starts? That's where control flow comes in to change the
course of the program. Control flow is necessary because we can't expect
everything to be like a set of instructions. Changes have to be made. For
example, we can say, "Jump off the building if it is on fire, else
continue typing your report." The statement above accomplishes something a
list of instructions just can't do - change the direction. [Beginner - Introduction to Programming] <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Flow of control: the <b>order</b> in which the individual
statements, instructions or function calls of an imperative or a declarative
program, are <b>executed</b> or evaluated.
[Control flow]<o:p></o:p></span></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.2.3.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Terminating condition: <o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;">Without
terminating condition, computer will run to infinity. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<h2>
<!--[if !supportLists]-->1.3. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Computer</h2>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;">The word
“computer” was recorded firstly in 1613 in a book called “The yong mans
gleanings” by English writer Richard Braithwait: <i>I haue read the truest computer of Times, and the best Arithmetician
that euer breathed, and he reduceth thy dayes into a short number</i>. It
referred to a person who carried out calculations, or computations, and the
word continued with the same meaning until the middle of the 20th century. From
the end of the 19th century the word began to take on its more familiar
meaning, a machine that carries out computations. [Computer]<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;">Now days, to
execute the program, we can design a circuit that do exactly what the program
tells. This kind of device is called computer. Based on the flexibility of the
program, we can classified computer in two main type. </span></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.3.1.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Fixed program computers<o:p></o:p></span></h3>
<div class="MsoNormal" style="mso-list: none; text-align: justify; text-indent: .5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
first kind computing machine was fixed program computer. It is design to do
specific thing. Most of this early computer were tools to solve specific
mathematic problem [Guttag, 2013]. Example:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo9; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">A
revolutionary difference engine, designed to aid in navigational calculations,
by Charles Babbage, an English mechanical engineer and polymath, in early 19th
century (1833). [Computer] <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo9; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">In
1941, built by Atanasoff and Berry Computer (ABC) to solve system of linear
equation only. [Guttag, 2013] <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo9; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Alan
Turing bombe machine, (during World War II), design strictly for breaking
German Enigma Code. [Guttag, 2013] <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo9; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">ENIAC
(Electronic Numerical Integrator and Computer)<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo9; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">(Now
day) A four-function calculator only to solve basic mathematics only. (+, –, ×,
÷ ) [Guttag, 2013]<o:p></o:p></span></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.3.2.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Stored program computers<o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The <b>theoretical
basis</b> for the stored-program computer was laid by Alan Turing in his 1936
paper, <i>On Computable Numbers, with an Application
to the Entscheidungsproblem</i> [Computer]. In
1945 Turing joined the National Physical Laboratory and began work on
developing the principle of electronic stored-program digital computer. His
1945 report ‘Proposed Electronic Calculator’ was the first specification for
such a device. </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;">In that proposal he
described a hyphothetical computing device that has come to be called a
Universal Turing machine. The machine had an unbounded memory in the form of
tape on which one could write zeros, ones and some primitive instruction such
as moving, reading and writing to the tape. (remember, Turing machine is not
the same as Universal Turing Machine).</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="color: #00b050; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The difference in stored program
computer and fixed program computer rest not only in hardware but also in the programming
and use of machines [Olley, 2010]. With Universal Turing Machine, Turing
proposed that program can be treated and stored as data. Now, data and program
are the same, and because of program can produce data, it means program can
produce program. <span style="color: #00b050;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"><span style="color: #00b050;"> </span>
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;">It is still debated until
now about the first stored program computer. And John von Neumann, a leader in
continuum research at Princeton University, was offered a post-doctoral
position to Turing. But Turing decide to go back to England, help his state in war
with Nazi. Neumann see the idea of Universal Turing Machine and circulated his
First Draft of a Report on the EDVAC in 1945 [Computer]. Neumann success to put instruction
and data in the same memory. This<b> architecture</b>
is use widely in the CPU now day (See Figure 3). </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Consequently,
this principle can be used to describe and accomplish anything you can do with
computer, by executes any legal set of instruction.<span style="color: #00b050;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
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</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
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</span></span><!--[endif]--><span style="color: #00b050; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMJ9Hw8pzPCP97-QpAGLyFwhBZH5uMlkrI6eic1X6_ZZ_f7jfOtlDChLlarKHVOPtGTzvv6eKTb_5E3k2jU3usbIUIaf4mlp4Wc5aPhdUxWtqYN5Sw9jij72GP8bM41NHZd7-KtIWb9TJ3/s1600/3+-+Von+Neumann+Computer+Architecture.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMJ9Hw8pzPCP97-QpAGLyFwhBZH5uMlkrI6eic1X6_ZZ_f7jfOtlDChLlarKHVOPtGTzvv6eKTb_5E3k2jU3usbIUIaf4mlp4Wc5aPhdUxWtqYN5Sw9jij72GP8bM41NHZd7-KtIWb9TJ3/s1600/3+-+Von+Neumann+Computer+Architecture.jpg" height="288" width="320" /></a></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Figure
2. Stored program computer Architecture;</span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"><span style="color: #00b050;"> </span>
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;">The first
truly modern computer was The Manchester Mark 1, that built at the University
of Manchester, and its first programe in 1949. It implemented ideas previously
describe by John Von Newmann and Alan Turing.</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<h2>
<!--[if !supportLists]-->1.4. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Programming Language</h2>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">From section 1.2, we see that, programming
language provide a set of primitive instruction and primitive control structure.
The natural language which can be directly understood by the system is a
machine language. In machine language, a program is written in 1s and 0s
(binary code). So, a set of instruction in binary pattern is associated with
each computer. It is difficult to human like us to communicate with computer in
term of binary code. Hence, writing a program with a machine language is very
difficult. Moreover speed of writing, testing and debugging is very slow in
machine language. Changes of making careless error are bound to be there in
this language. Each type of hardware platform design, define a different type
of machine language. So, machine language is tedious and time consuming. [Kamthane, 2011]<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">To cope with that, people try to create
other type of languages. All other languages are said to be <i>high level</i> or <i>low level</i> according to how closely they can be said to resemble
machine code.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">These type of language are
classification as follows:<o:p></o:p></span></div>
<h3>
<!--[if !supportLists]-->1.4.2.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Assembly Language</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Instead of using a string binary bits in
a machine language, computer manufacturers started to providing something that
more easy to interpreted by programmers. So, the computer manufacturers started
providing mnemonics (English-like word abbreviated) that are similar to binary
instruction in machine languages. The program is in alphanumeric symbols like
ADD, SUB, MUL, DIV, RCL and RAL, called mnemonics. The designer chooses easy
that are to be remembered by the programmer, so that the programmer can easily
develop the program in assembly language. [Kamthane,
2011]<span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Here are some characteristics of the
assembly languages:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l3 level5 lfo11; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">-<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Less time consuming for an assembler to
write and then test the program, rather than in machine language.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l3 level5 lfo11; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">-<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Assembly languages programs are not
portable, cause each type of processor has its own assembly language. For
example, 8085 CPU has its own assembly language, CPUs such as 8086, 80186,
80286 have their own assembly languages.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l3 level5 lfo11; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">-<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Assembly language is a low-level
language corresponds closely to machine code, so that a single low-level
language instruction translates to a single machine-language instruction.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l3 level5 lfo11; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">-<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Efficient (optimum use of both computer
memory and processing time) for short and simple program, cause to write a
low-level program takes a substantial amount of time.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l3 level5 lfo11; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">-<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">It is necessary to remember and
understand inner workings of the processor, the registers of CPU and mnemonic
instructions by the programmer.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<h3>
<!--[if !supportLists]-->1.4.3.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->High-level Language</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">As we see before, some assembly
languages characteristics are disadvantages for programmer. Don’t worry,
because high-level languages will overcome this problem. High-level languages
are build base on procedure oriented languages. These languages are employed
for easy and speedy development of a program. Examples of high-level language
are COBOL, FORZTRAN, BASIC, C and C++. [Kamthane,
2011]<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Following are some characteristics of
high-level languages:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l7 level5 lfo12; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">+<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Less time consuming for program
development than assembly language.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l7 level5 lfo12; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">+<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Several mnemonic instructions are needed
to write in assembly language than a single line in high-level language. Thus, high
language programs are shorter than the assembly language programs.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l7 level5 lfo12; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">+<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Testing and debugging a program is
easier than in the assembly language<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l7 level5 lfo12; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">+<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Portability of a program from one
machine to other<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<h2>
<!--[if !supportLists]-->1.5. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Programming Translator</h2>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">A program can be written in <b>assembly language</b> as well as in <b>high-level language</b>. This written
program is called the source program. The <b>source
program</b> is to be converted to the machine language, which is called an <b>object program</b>. All computer programs
run on machine code that is executed directly on computer architecture. Machine
code is not easily read or programmed directly by humans. Essentially, machine
code is a long series of bits (i.e. ones and zeroes). In order to program,
humans write code in a language that is then translated in to machine code.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Program translator translates source
code of programming language into machine language-instruction code. Generally,
computer programs are written in languages like COBOL, C, BASIC and ASSEMBLY
LANGUAGE, which should be translated into machine language before execution.
Programming language translators are classified as follows [Kamthane, 2011]:<o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<br /><!--[endif]--></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhu3uOxx_j8dqET5OXR2kWOgWcEAhPofdf4e0gNJA_YFHLDRDKHrXltTi9r1_OVT9Iv5IP0sSa161vjwIVrZS_xVI9JkJPmt47Q8uxX0uWGkdrPyJ5xaKTUOcPEXnBXqiq3KobwWZCjnVUk/s1600/3+-+Program+language+translator.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhu3uOxx_j8dqET5OXR2kWOgWcEAhPofdf4e0gNJA_YFHLDRDKHrXltTi9r1_OVT9Iv5IP0sSa161vjwIVrZS_xVI9JkJPmt47Q8uxX0uWGkdrPyJ5xaKTUOcPEXnBXqiq3KobwWZCjnVUk/s1600/3+-+Program+language+translator.jpg" height="117" width="320" /></a></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Figure
3. Programming language translator classification;</span></div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.5.1.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Assembler<o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The translation job is performed either
manually or with a program called assembler. In hand assembly, the programmer
uses the set of instructions supplied by the manufacturer. In this case, the
hexadecimal code for the mnemonic instruction is searched from the code sheet.
This procedure is tedious and time-consuming. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Alternate solution to this is the use of
assemblers, the program that provides the codes of the mnemonics. An assembler translates
the symbolic codes of programs of an assembly language into machine language
instructions (see Figure 4a). The reasons why assembly language is efficient
for small program because, with assembler, assembly language is translated in
the ratio of one to one. It mean one mnemonics instructions will translate to
one machine code instructions. [Kamthane, 2011]<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: center;">
<br /><!--[endif]--></div>
<div class="MsoNormal" style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5qWDmc8_LhFKabrIeiHgug1J7YKNczf17swD1uom0GyfCtMFguv-Lwbfsg4NN4z48lFFg66wFgGjCBu54kB6OkZzr81c96UT5gsDtq2F4XfGAdfWd9HzgEAjLSOuBYfMHwEoQ9qwNVN0X/s1600/4a+-+Translator+Process+(Assembler).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5qWDmc8_LhFKabrIeiHgug1J7YKNczf17swD1uom0GyfCtMFguv-Lwbfsg4NN4z48lFFg66wFgGjCBu54kB6OkZzr81c96UT5gsDtq2F4XfGAdfWd9HzgEAjLSOuBYfMHwEoQ9qwNVN0X/s1600/4a+-+Translator+Process+(Assembler).jpg" height="48" width="400" /></a></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Figure
4a. Assembler translation process;</span></div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.5.2.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Compiler<o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Compilers are the translators for
high-level languages. Compile is a process to translate all the instructions of
the program into machine codes, which can be used again and again (see Figure
4b). The source program is input to the compiler. The object code is output for
the secondary storage device. The <b>entire
program</b> will be read by the compiler first and then generates the object
code. It is different from interpreter process, which we will see in the next
section. High-level languages such as C, C++ and Java use compiler as the translator. The compiler also displays the list of errors and warnings
for the statements violating the syntax rules of the language. Compilers also
have the ability of linking subroutines of the program. [Kamthane,
2011]<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: center;">
<br /><!--[endif]--></div>
<div class="MsoNormal" style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5H3zTfxAi5N5p2pf3DKFMGoKVptky1bvOkVdg2yE-QL2ET7A3MVBlPbzEjBCiX3nanddAwggvBxXhSYjJANjqgAk2nfbYfXv5mbNID0bRZkTUyBGX5qwd79tugEFomGnmfV8hhU-3taDT/s1600/4b+-+Translator+Process+(Compiler).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5H3zTfxAi5N5p2pf3DKFMGoKVptky1bvOkVdg2yE-QL2ET7A3MVBlPbzEjBCiX3nanddAwggvBxXhSYjJANjqgAk2nfbYfXv5mbNID0bRZkTUyBGX5qwd79tugEFomGnmfV8hhU-3taDT/s1600/4b+-+Translator+Process+(Compiler).jpg" height="48" width="400" /></span></a></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Figure
4b. Compiler translation process;</span></div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1.5.3.<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">Interpreter<o:p></o:p></span></h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;">Interpreters
also come in the group of translators for high-level languages. Same with
compiler, the interpreter source program is just like English statements. But
interpreter have different in translate process. The interpreter generates
object codes by <b>reads and translate</b>
the source program <b>line by line</b>.
Interpreter directly executes the program from its source code. Due to this,
every time the source code should be inputted to the interpreter. In other
words, each line is converted into the object codes. It takes very less time
for execution because no intermediate object code is generated. [Kamthane,
2011] <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">M-BASIC, Python are examples of interpreter.</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-size: 11.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: center;">
<br /><!--[endif]--></div>
<div class="MsoNormal" style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA4O-o3ZLaAq-u4Uhn-O_fXkNZwRMcjEvjOTlZvL1OZo3P3h2Oe81T7K-B4xya_vcCu0AK0ccbpGTpd8P4bHDIgRq_YEnozruEsya92Y52flURPXWsWz37O5lWr8LAKdsxL4lfW45FwQix/s1600/4c+-+Translator+Process+(Interpreter).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA4O-o3ZLaAq-u4Uhn-O_fXkNZwRMcjEvjOTlZvL1OZo3P3h2Oe81T7K-B4xya_vcCu0AK0ccbpGTpd8P4bHDIgRq_YEnozruEsya92Y52flURPXWsWz37O5lWr8LAKdsxL4lfW45FwQix/s1600/4c+-+Translator+Process+(Interpreter).jpg" height="48" width="400" /></span></a></div>
<div align="center" class="MsoNormal" style="mso-list: none; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Figure
4c. Interpreter translation process;</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<h2>
<!--[if !supportLists]-->1.6. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Programming Language Aspects/Elements – an English
sentence analogy</h2>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Just like natural languages (ex,
English, Chinese, Indonesian, etc), each programming languages has a set of
primitive construct. The aim of this construct is to produce well form program,
that <b>has exactly only one meaning</b>.
This set of construct consist of:<o:p></o:p></span></div>
<h3>
<!--[if !supportLists]-->1.6.1.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Syntax</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The Syntax of a language refers to the
spelling of the program, which strings/sequences of characters and symbols are
well formed. For example, in English the string "ball shirt boy" is
not a syntactically valid sentence, because the English grammar does not accept
sentences in the form of <noun> <noun> <noun>. In Python syntax
chart, the sequence of primitive 3.5 + 3.5 is syntactically well form, but the
sequence 3.5 3.5 is not.<o:p></o:p></noun></noun></noun></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">We discuss syntax first, because syntax
errors are the most common kind of error, but it is the least dangerous kind of
error. A good programming language does a complete job of detecting syntactic
errors, and will not allow users to execute a program with even one syntactic
error. Furthermore, in most cases the language system
gives a sufficiently clear indication of the location of the error that it is
obvious what need to be done to fix it. [Guttag,
2013]<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<div class="MsoListParagraph" style="text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<h3>
<!--[if !supportLists]-->1.6.2.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Static semantics</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The static semantics refer to syntactically
valid strings that have a meaning. For example,
the English string "I are big" is of the form <pronoun>
<linking verb=""> <adjective>, which is syntactically acceptable sequence.
However, it is a static semantic error, because the noun "I" is singular
and the verb "are" is plural. So it doesn’t have a real meaning. In Python, the sequence 3.7/'abc' is syntactically
well formed (<literal> <operator> <literal>), but produce a
static semantic error, because dividing a number by a string of characters is
not meaningful. <o:p></o:p></literal></operator></literal></adjective></linking></pronoun></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Semantic errors, is a bit more complex
than syntax. Static semantic error makes program behavior become unpredictable,
so it is important to do static semantic checking. Some programming languages,
e.g., java, do a good job on static semantic checking before allowing a program
to be executed. Others, e.g., C and Python, do relatively
less static semantic checking. Python does do a considerable amount of static
semantics checking while running a program. However, it does not catch all
static semantic errors. [Guttag, 2013]<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<div class="MsoNormal">
<br /></div>
<h3>
<!--[if !supportLists]-->1.6.3.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Semantics</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Semantics is talk about, what that
meaning of the program. The special in programming language is that every well-formed
program, which free of syntax and static semantics error, will only has exactly
one meaning. Different with, natural languages, e.g., English, can be
ambiguous. For example, the sentence "I cannot
praise this student too highly" can be either flattering or damning. [Guttag, 2013]<o:p></o:p></span></div>
<div class="MsoNormal" style="mso-list: none; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="mso-list: none; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span></div>
<h2>
<!--[if !supportLists]-->1.7. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Paradox of computer program</h2>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">As we see before, program has no
syntactic error and no static semantic error, it has a meaning, i.e., it has semantics
and computer will do exactly what <b>you
tell</b> it to do. This is <u>good news</u>. But semantic doesn’t mean that computer
will do exactly as <b>what the programmer
want</b> it to do. When a program done something other than what its creator
thinks it means, <u>bad things</u> can happen. Now we see the paradox.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The following are what happen when a
computer do something other than programming meaning, in order of badness: <o:p></o:p></span></div>
<h3>
<!--[if !supportLists]-->1.7.1.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Crash</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;">At the lowest level, it might
crash, or in other words, it stops running and produces some sort of indication.
In a properly designed computing system, when a program crashes it doesn’t
damage to the overall system. Of course, some very popular computer systems don't
have this nice property. Almost everyone who uses a personal computer has run a
program that has managed to make it necessary to restart the whole computer. </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">[Guttag, 2013]</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></div>
<h3>
<!--[if !supportLists]-->1.7.2.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Never stop</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Next level, it might keep running, and
running, and running, and never stop (or called infinity loop). This situation
is hard to recognize if we have no idea about how long the program is supposed
to take to do its Job.<span style="color: red;"> </span>[Guttag, 2013]<span style="color: red;"><o:p></o:p></span></span></div>
<h3>
<!--[if !supportLists]-->1.7.3.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Run to completion but produce wrong answer</h3>
<div class="MsoNormal" style="margin-left: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The worst thing can happen is when the program
run to completion and produce an answer that might be correct, or might not. This
is very bad, cause when a program appear to be doing the right thing but isn't,
disaster can follow. Example: fortunes can be lost, patients can receive fatal
doses of radiation therapy, airplane can crash, etc. So it is important to
programmer when they write a program, it should be written in such a way that
when it doesn't work properly, it is self-evident. [Guttag, 2013]<o:p></o:p></span></div>
<h2>
<!--[if !supportLists]-->1.8. <span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Why we use python in learning computer science???</h2>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin: 0in; text-align: justify; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">There are many sources and reasons for
us to use python as a programming learning tool. These are some conclusions of
the reasons we choose Python:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l6 level5 lfo15; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Medioker<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l6 level5 lfo15; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Easy to use<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l6 level5 lfo15; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Widely use<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l6 level5 lfo15; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Easy to debug<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l6 level5 lfo15; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Interpreter (we can compile python but
it is unusual & un-efficient)<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l6 level5 lfo15; text-align: justify; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Better learning curve<o:p></o:p></span></div>
<div class="MsoNormal" style="mso-list: none; text-align: justify;">
<br /></div>
<h1 align="center" style="margin-bottom: 12.0pt; margin-left: 0in; margin-right: 0in; margin-top: 24.0pt; text-align: center; text-indent: 0in;">
Bibliography<w:sdtpr></w:sdtpr></h1>
<div class="MsoBibliography" style="mso-list: none; text-indent: .5in;">
<!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>BIBLIOGRAPHY <span style='mso-element:field-separator'></span><![endif]--><i>Algorithm Analysis.</i> (n.d.). Retrieved June 12, 2013, from http://courses.cs.vt.edu/:
http://courses.cs.vt.edu/cs2604/spring04/Notes/C04.AlgorithmAnalysis.pdf<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>Algorithm vs.
Computer Program</i>. (n.d.). Retrieved
June 12, 2013, from http://www.coderanch.com/:
http://www.coderanch.com/t/396727/java/java/Algorithm-computer-program<o:p></o:p></div>
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<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>Beginner -
Introduction to Programming</i>. (n.d.).
Retrieved January 31, 2013, from library.thinkquest.org:
http://library.thinkquest.org/15375/b01.htm<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>Computer</i>. (n.d.). Retrieved February 19, 2014, from
wikipedia.org: http://en.wikipedia.org/wiki/Computer<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>Control flow</i>. (n.d.). Retrieved January 8, 2013, from
en.wikipedia.org: http://en.wikipedia.org/wiki/Control_flow<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>Declarative
Programming</i>. (n.d.). Retrieved
January 8, 2013, from en.wikipedia.org:
http://en.wikipedia.org/wiki/Declarative_programming<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]-->Guttag, J. V.
(2013). <i>Introduction to Computation and Programming Using Python</i>
(spring 2013 ed.). Cambridge, Massachusetts: The MIT Press.<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>Imperative
Programming</i>. (n.d.). Retrieved
January 8, 2013, from en.wikipedia.org:
http://en.wikipedia.org/wiki/Imperative_programming<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]-->Kamthane, A.
(2011). <i>PROGRAMMING IN C</i> (2nd Edition ed.). (R. Sachdev, Ed.) India:
Pearson Education India.<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]-->Olley, A. (2010).
Existence Precedes Essence - Meaning of the Stored-Program Concept*. <i>IHPST,
University of Toronto</i> , 10.<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>Programming
Languages - Instructions</i>. (n.d.).
Retrieved June 14, 2013, from http://en.kioskea.net/:
http://en.kioskea.net/contents/313-programming-languages-instructions<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]-->Rouse, M. (2005,
September). <i>DEFINITION - Instruction</i>. Retrieved June 9, 2013, from
http://searchcio-midmarket.techtarget.com:
http://searchcio-midmarket.techtarget.com/definition/instruction<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>What is a
computer algorithm?</i> (n.d.). Retrieved
June 12, 2013, from http://www.howstuffworks.com:
http://www.howstuffworks.com/question717.htm<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 0in; text-indent: 0in;">
<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><i>What is the
differences between algorithm and program?</i> (n.d.). Retrieved June 12, 2013, from http://wiki.answers.com/:
http://wiki.answers.com/Q/What_is_the_differences_between_algorithm_and_program<o:p></o:p></div>
<div class="MsoNormal" style="margin-left: 0in; text-indent: 0in;">
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</span><!--[endif]--><!--[if supportFields]><span style='mso-element:
field-end'></span><![endif]--><o:p> </o:p></div>
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<w:sdt docparttype="Bibliographies" docpartunique="t" id="32540577" sdtdocpart="t">
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<!--[if !supportLists]--><span style="font-size: 7pt;">
</span><!--[endif]--><a href="file:///D:/Hobby/Bahan%20Kuliah%20MIT/Electrical%20Engineering%20and%20Computer%20Science/MIT%206.00SC%20Introduction%20to%20Computer%20Science%20and%20Programming,%20Spring%202011/Lecture%201/Sky%20Note/Ch1%20-%20Introduction%20to%20Computer%20Science%20(2014%2007%2021).docx#_ftnref1" name="_ftn1" title=""><span class="MsoFootnoteReference"><!--[if !supportFootnotes]--><span class="MsoFootnoteReference"><span style="font-family: "Calibri","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">[1]</span></span><!--[endif]--></span></a>
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Many
believe that Heron was not Inventor of this method, and indeed there is some
evidence that it was well known to the ancient Babylonians. [Guttag, 2013]</span></div>
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skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com1tag:blogger.com,1999:blog-9034572127535224290.post-1620464974874258292014-03-21T02:04:00.000-07:002014-03-21T08:34:51.763-07:00Galaxy S5 US$ 100 More Expensive Than S4 at Launch (Indonesia)Today (22/3), SEIN (Samsung Electronics Indonesia) start to selling its flagship, Samsung Galaxy S5. Joining with Erafone, a giant electronics retailer in Indonesia, present the galaxy S5 (SIM unlock model) with price Rp 8.500.000,- (about US$ 777 or EUR564).<br />
Different with <a href="http://www.gsmarena.com/samsung_galaxy_s5_to_be_60_cheaper_than_s4_at_launch-news-8086.php">Taiwanese and some "rumors" price</a> , Samsung Galaxy S5 in Indonesia is almost $100 more expensive than Samsung Galaxy S4 price at the launcing, but still cheaper than Note 3 at launching.<br />
<br />
As usual Indonesia will only get Exynox model (see the spesification on the ad picture). Rest of the spesification are 5.1" full HD super AMOLED, 16MP main shooter and 2MP front camera for selfi of videocall.<br />
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We can get another extra bonus for some term & condition.<br />
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skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-8859992923458291422012-09-07T05:53:00.001-07:002012-09-07T06:06:29.934-07:00Kamus istilah (British English - Bahasa Indonesia)<br />
<ul>
<li>“Household Name” : is someone or something that is recognized by most people (famous). So, if you walk into an average household and mention the name, people will know who you're referencing. Household name dalah ungkapan dalam Bahasa Inggris yang berarti nama (seseorang atau sesuatu) yang sangat terkenal, bahkan hampir setiap rumah tangga mengenali ketika kita menyebutkan nama tersebut.</li>
</ul>
skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-44492208214275804662012-08-29T17:12:00.005-07:002012-08-30T05:17:20.135-07:00Samsung dan Android Melanjutkan Pembangunan ‘Galaxy Technology’, Microsoft Tidak Mau Ketinggalan<br />
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<span style="text-indent: 27pt;">Perhelatan IFA 2012 di Berlin
belum genap satu hari dibuka namun tampaknya puncak dari acara tersebut telah ‘dicuri’
oleh Samsung Electronics. Meskipun beberapa hari lalu pukalan keras dari Apple
melalui pengadilan Amerika Serikat cukup membuat saham Samsung menurun, tampaknya
kini perusahan teknologi asal negeri ginseng tersebut telah mendapatkan kembali
tangga menuju puncak. Mata ribuan penonton dan jurnalis yang hadir dalam IFA
2012 Berlin (29/8), benar-benar ‘disihir’ dengan kehadiran dua gadget terbaru besutan
Samsung dan si robot hijau Android. Tidak lain adalah Samsung Galaxy
Note II yang kehadirannya semakin makin memantapkan jati diri dan medefinisikan phone-tablet, serta
Samsung Galaxy Camera yang tampaknya akan menjadi ancaman serius bagi Nokia
PureView.</span></div>
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<span style="text-indent: 27pt;">Dari segi tampilan luar, sang
penerus tidak banyak mengalami perubahan dibandingkan pendahulunya, Galaxy
Note. S-Pen yang dihadirkan jauh lebih presisi, dan memiliki sensifitas tekanan
yang luar biasa, dan sedikit lebih tebal, tetapi </span><i style="text-indent: 27pt;">body</i><span style="text-indent: 27pt;"> Note II secara keselurah sedikit lebih tipis. Dalam hal display, Note
II mulai menggunakan layar Super AMOLED HD, lebih besar 2”, tetapi resolusinya
sedikit berkurang dibandingkan generasi sebelumnya. Layar Dapur pacu Galaxy Note
II banyak yang diadaptasi dari Galaxy SIII, hanya mengalami penigkatan RAM
menjadi 2GB. Dalam hal perangkat lunak, Note II mulai menerapkan kemampuan </span><i style="text-indent: 27pt;">multitasking</i><span style="text-indent: 27pt;">, dan air view yaitu
kemampuan untuk menampilkan sebagian deskripsi dari foto, </span><i style="text-indent: 27pt;">plan</i><span style="text-indent: 27pt;">, atau </span><i style="text-indent: 27pt;">e-mail</i><span style="text-indent: 27pt;"> cukup
dengan mendekatkan S-Pen di atas </span><i style="text-indent: 27pt;">item</i><span style="text-indent: 27pt;">
yang diinginkan tanpa menyentuh </span><i style="text-indent: 27pt;">item</i><span style="text-indent: 27pt;">
tersebut. </span></div>
<div style="text-align: justify;">
<a href="http://www.samsung.com/galaxynote2" style="text-indent: 27pt;">Spesifikasi Lengkap Samsung Galaxy Note II</a><span style="text-indent: 27pt;"> </span><br />
<a href="http://blog.gsmarena.com/which-is-the-brightest-star-in-the-samsung-galaxy-galaxy-note-ii-vs-galaxy-s-iii-vs-galaxy-note/" style="text-indent: 0in;">Perbandingan Galaxy Note II vs Galaxy SIII vs GalaxyNote</a><br />
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Dengan basis, Samsung Galaxy SIII
yang cukup sukses, Samsung menghadirkan <a href="http://www.samsungmobilepress.com/2012/08/29/Samsung-presents-10281979Camera,-Reborn.10281979-the-GALAXY-Camera">Galaxy Camera</a> salah satu kamera ber<i>platform</i> android. Tidak seperti nokia
808 pureview yang memiliki resulusi hingga 41MP, Galaxy Camera hanya memiliki
memiliki resolusi 16MP, tetapi dengan kemampuan <i>optical zoom</i> hingga 21 kali. Pernah melihat foto berikut? </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWD1lyxJFW_mD7t5e-c4mEOW2FtRKa9wLzDGbWqJ5Y0gYDanpsAyqGpE_F_60MEbyXqRA_Gp0P1Bd-gMUEPcQcSB8M1_v7YR2W_xtME86tMK9gF31sVeDcahmHbjL_fdQIFfp8cr4yf0A5/s1600/Gambar+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWD1lyxJFW_mD7t5e-c4mEOW2FtRKa9wLzDGbWqJ5Y0gYDanpsAyqGpE_F_60MEbyXqRA_Gp0P1Bd-gMUEPcQcSB8M1_v7YR2W_xtME86tMK9gF31sVeDcahmHbjL_fdQIFfp8cr4yf0A5/s1600/Gambar+2.jpg" /></a></div>
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<i><span style="font-size: 9.0pt; line-height: 150%; mso-bidi-font-size: 12.0pt;">Sumber: <a href="http://komunitaslightgraffiti.blogspot.com/">http://komunitaslightgraffiti.blogspot.com/</a><o:p></o:p></span></i></div>
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Mengkin kita
berpikir bahwa untuk mendapatkan hasil seperti gambar tersebut kita harus
menggunakan kamera DSLR seperti yang dimiliki para <i>professional photographer</i>. Jangan kaget, karena dengan teknologi <i>Smart Pro</i> yang ditanamkan pada Galaxy
Camera, kita bisa menghasilkan foto seperti itu. <i>Feature Smart Pro</i> juga memungkinkan kita menangkap <i>image</i> dari benda yang bergerak secara
lebih baik. Teknologi <i>Smart Pro</i> menjadikan
siapapun yang menggunakan Galaxy Camera akan mudah untuk menghasilkan foto, layaknya
foto yang dibuat seorang profesional. </div>
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Anda dapat menggunakan perintah
suara untuk mengambil gambar, mengatur <i>zoom</i>,
bahkan mengatur <i>timer</i>. Anda juga dapat
langsung mengatur folder, memberi <i>tag</i>
atau bahkan meng<i>edit</i> foto pada Galaxy
Camera. Dengan Bluetooth 4.0, WiFi, 3G/4G, <i>sharing</i>
foto kepada perangkat lain, facebook, atau blog pribadi, mejadi hal yang mudah.</div>
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Kedua gadget baru ini benar-benar memperkuat Galaxy series yang dibangun Samsung
bersama Android. Jika Anda ingin menggunakan smarphone dan dompet, Galaxy Nexus
dan Galaxy SIII rajanya. Saat Anda membutuhkan note, Galaxy Note II siap anda
coret-coret. Saat Anda membutuhkan Table, Galaxy Tab dan Galaxy Note 10.1 siap
menemani. Jika anda membutuhkan proyektor, Samsung pun telah menyediakan <a href="http://www.samsung.com/global/microsite/galaxybeam/">Galaxy Beam</a> bagi Anda. Bahakan saat Anda membutuhkan mp3, <i>portable console game</i> sekaligus <i>video
player</i> yang cukup lega, sudah ada <a href="http://www.samsung.com/us/mobile/galaxy-players">Galaxy Player</a>. Kini Samsung telah
menyediakan SMART TV yang dapat dikendalikan dari HP Android Anda, bukan tidak
mungkin kedepan Samsung akan segera meluncurkan TV ber-<i>platform</i> Android, seperti halnya <a href="http://www.samsung.com/us/appliances/refrigerators/RF4289HARS/XAA">RF4289HARS</a> (<a href="http://www.youtube.com/watch?v=ZAhiHY5KtXk&feature=related">lemari pendingin Samsung yang dilengkapi dengan Android <i>operating system</i></a>). </div>
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Microsoft tidak tinggal diam melihat
kesuksesan Samsung bersama Android. Walaupun Nokia sering dianggap sebagai ‘anak
emas’ dalam pembangunan Windows operating system, Microsoft nampaknya mulai mencoba
peruntungan dengan mengikut sertakan Samsung dan beberapa produsen gadget lainnya.
Hal ini terbukti dengan diluncurkannya <i>smartphone</i>
pertama di dunia yang menggunakan Windows Phone 8 OS adalah <a href="http://www.samsungmobilepress.com/2012/08/29/Samsung-Ready-to-Go-With-Windows-8-and-Windows-Phone-8">Samsung ATIV S</a>, meskipun Windows 8 belum dirilis secara resmi oleh Microsoft. Pada perhelatan
IFA 2012 ini juga Samsung telah meluncurkan tablet (<a href="http://www.samsungmobilepress.com/2012/08/29/Samsung-Ready-to-Go-With-Windows-8-and-Windows-Phone-8">Samsung ATIV Smart PC dan Samsung ATIV Smart PC Pro</a>) beserta ultrabook (<a href="http://www.samsung.com/id/consumer/computers-printer/notebook-pc/high-performance/NP900X3C-A02ID?cid=id_sem_series9_q3_240731082012">Samsung 9 Series</a> terbaru), yang semuanya
berjalan pada windows 8.</div>
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Dengan Windows 8, Microsoft
berusaha untuk menyamakan kernel yang digunakan baik pada smartphone yang
menggunakan prosesor ARM maupun pada PC yang menggunakan prosesor Intel. Microsoft
berusaha untuk menyatukan para developer, agar kelak aplikasi pada PC dapat
dijalankan dengan baik juga pada smartphone. Namun Windows 8 ini bersifat
tertutup sehingga untuk menginstall aplikasi Anda harus mengambilnya melalui
marketplace dan Windows wajib mendapatkan sebagian dari keuntungan penjualan
aplikasi tersebut. </div>
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Melihat arah pergerakan Microsoft
ini, maka Android sebagai penguasa ‘pasar’ <i>open
source</i> tampaknya mulai berusaha untuk berdamai dengan saudara dekatnya, Linux, untuk mengembakan dan mempertahankan ‘pasar’
<i>open source</i>. Tampaknya perkembangan
dan peperangan di industri teknologi ini akan semakin menarik.</div>
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skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-79280000541122160012012-08-24T22:18:00.004-07:002012-08-27T11:57:39.554-07:00MENG-INSTALL PYTHON PADA WINDOWS<br />
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<h2>
<a href="http://www.blogger.com/blogger.g?blogID=9034572127535224290" name="_Toc250721772"><!--[if !supportLists]-->1.1.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Berkenalan dengan Pyhton</a></h2>
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<div style="text-align: center;">
<span style="text-align: center; text-indent: 0in;">Gambar 1. Phyton</span></div>
<span style="text-align: center; text-indent: 0in;"><br /></span>
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Python
adalah salah satu jenis bahasa pemrograman tingkat tinggi. Bahasa pemrograman
tingkat tinggi adalah bahasa pemrograman yang dirancang untuk lebih memudahkan
manusia sebagai pengguna (<i>user</i>),
dalam berhubungan dengan mesin. Selain Python bahasa pemrograman tingkat tinggi
lainnya seperti C, C++, Pearl, Java, MatLab, dan lain-lain. Sebagai bahasa
tingkat tinggi, Phyton bersifat <i>portable</i>,
artinya dapat digunakan pada berbagai jenis komputer dengan sedikit atau bahkan
tanpa modifikasi.</div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Sebaliknya
bahasa pemrograman tingkat rendah (bahasa mesin atau bahasa <i>assembly</i>), umumnya, hanya dibuat untuk
memprogram 1 jenis <i>hardware</i> saja.
Bahasa mesin memang dirancang untuk mudah dimengerti oleh mesin (komputer) itu
sendiri. Penulisan program dengan bahasa mesin akan jauh lebih panjang
dibandingkan penulisan program dengan bahasa tingkat tinggi.</div>
<div class="MsoNormal" style="margin-bottom: 12pt; text-align: justify; text-indent: 27pt;">
Pengguna bahasa pemrograman tingkat tinggi perlu
menterjemahkan <i>source code</i>-nya ke
dalam bahasa pemrograman tingkat rendah yang dapat dimengerti oleh mesin.
Secara garis besar, ada dua metode untuk menerjemahkan bahasa tingkat tinggi ke
dalam bahasa tingkat rendah, yaitu <i>compiling</i>
dan <i>interpretation</i>. Pyton menggunakan
prosses <i>interpretation</i> untuk mengubah
bahasa tingkat tingginya menjadi bahasa yang dimengerti mesin. Bagan dibawah
ini akan memperlihatkan perbedaan prosess <i>compiling</i>
dan <i>interpretation</i>.</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibUsai1r9rXpKGzLcouo2XJiaek6EqIMmeF3uxIGChIuE7SN-OhgNhifOBPRtxPauJRvyPPINNlzMgDeEda3MVHMf42EfMESFcTT6DPld86gr7ZUV_Nvj7kaFMqP4w46otKaF-afn0wSAi/s1600/Gambar+2+-+Interpreter+vs+Compiler.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="438" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibUsai1r9rXpKGzLcouo2XJiaek6EqIMmeF3uxIGChIuE7SN-OhgNhifOBPRtxPauJRvyPPINNlzMgDeEda3MVHMf42EfMESFcTT6DPld86gr7ZUV_Nvj7kaFMqP4w46otKaF-afn0wSAi/s640/Gambar+2+-+Interpreter+vs+Compiler.jpg" width="640" /></a></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<span style="text-indent: 27pt;">Gambar 2. </span><i style="text-indent: 27pt;">Interpreter</i><span style="text-indent: 27pt;"> vs </span><i style="text-indent: 27pt;">Compiler</i></div>
<div class="MsoNormal" style="text-align: center; text-indent: 0in;">
<i style="text-indent: 27pt;"><br /></i></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Gambar
diatas mungkin membuat sahabat semakin penasaran akan perbedaan <i>interpreter</i> dan <i>compiler</i>. <i>Interpreter</i>
akan langsung mengeksekusi baris demi baris dari program yang ditulis.
Sebaliknya <i>compiler</i> akan
menerjemahkan terlebih dahulu seluruh isi <i>source
code</i> menjadi <i>object code</i>, barulah
kemudian dieksekusi untuk menghasilkan keluaran. Walaupun <i>object code</i> yang yang dihasilkan dapat dijalankan ulang
berkali-kali, namun menciptakan <i>source
code</i> untuk sebuah <i>compiler</i> akan
jauh lebih kompleks dibandingkan <i>interpreter</i>. </div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Jika
sahabat mencari bahasa yang dapat digunakan pada berbagai <i>operating system platform</i>, gratis dan mudah diperoleh, maka <i>interpreter</i> seperti Python adalah
jawabannya. Dalam hal <i>syntax</i>, Python
memiliki <i>syntax</i> yang jauh lebih
sederhana dibandingkan bahasa tingkat tinggi lainnya seperti C, C++ atau Java.
Tidak hanya pemula atau programmer amatiran yang menggunakan Python, kalangan
professional pun banyak yang senang menggunakan Python, dan mereka memberikan
banyak dukungan bagi Python melalui berbagai komunitas. Kesederhanaan dalam hal
penulisan program, membuat para pemula dapat mempelajari pemrograman dengan
lebih mudah. Para profesional pun dapat memrogram secara cepat dengan
produktifitas keberhasilan yang tinggi, tetapi memiliki tingkat frustasi/stress
yang rendah. Menulis program dengan Python telah memberikan banyak kesenangan (<i>fun</i>). <span style="text-indent: 27pt;">Dan yang terpenting, Python itu GRATISSSSSSSSSSSSS
. . . . </span><span style="font-family: Wingdings; text-indent: 27pt;">J</span></div>
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Untuk melihat bagaimana sederhananya Python,
mari kita lihat perbandingan penulisan sebuah program yang mungkin sudah tidak
asing lagi bagi sahabat, yaitu menampilkan <i>text</i>
“Hello World!” pada layar. </div>
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Tabel
1. Perbandingan program ‘Hello World!’ pada Python dan C++</div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 5.4pt; mso-border-alt: solid black .5pt; mso-border-insideh: .5pt solid black; mso-border-insidev: .5pt solid black; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border: solid black 1.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 157.5pt;" valign="top" width="210"><div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<b>Python
2.x<o:p></o:p></b></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 265.5pt;" valign="top" width="354"><div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<b>C++<o:p></o:p></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 157.5pt;" valign="top" width="210"><div align="left" class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-indent: 0in;">
<span style="font-family: 'Courier New'; font-size: 10pt;">print
"Hello, World!"<o:p></o:p></span></div>
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<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 265.5pt;" valign="top" width="354"><div align="left" class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-indent: 0in;">
<span style="font-family: 'Courier New'; font-size: 10pt;">#include
<iostream .h=".h"><o:p></o:p></iostream></span></div>
<div align="left" class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-indent: 0in;">
<br /></div>
<div align="left" class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-indent: 0in;">
<span style="font-family: 'Courier New'; font-size: 10pt;"> void main()<o:p></o:p></span></div>
<div align="left" class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-indent: 0in;">
<span style="font-family: 'Courier New'; font-size: 10pt;"> {<o:p></o:p></span></div>
<div align="left" class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-indent: 0in;">
<span style="font-family: 'Courier New'; font-size: 10pt;"> cout << "Hello, world!"
<< endl;<o:p></o:p></span></div>
<div align="left" class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; text-indent: 0in;">
<span style="font-family: 'Courier New'; font-size: 10pt;"> }<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
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Tebel.1 menunjukan secara jelas perbedaan
panjang <i>script</i> dari sebuah program
yang sama dengan bahasa pemrograman yang berbeda. Untuk menjelaskan <i>script</i> program ‘Hello World!’ dengan
bahasa C++ mungkin membutuhkan sekitar 13 paragraf. Dengan Python, program
tersebut dapat dijabarkan dalam dua paragraf. Hal ini membuat kita bisa lebih
fokus untuk memahami pemrograman dan tidak membuang-buang waktu dalam penulisan
<i>syntax</i> yang rumit.</div>
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<br /></div>
<h2>
<!--[if !supportLists]-->1.2.<span style="font-size: 7pt; font-weight: normal;"> </span><!--[endif]-->Memilih
Phyton yang Sesuai</h2>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<b>Apa bedanya Pyton 2.x dengan Python 3.x?<o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Secara
singkat Python 2.x yang sedang menjadi “penguasa”, sedangkan Python 3.x adalah
masa depan dari Python yang sudah bisa digunakan sekarang. Python 2.x tidak
akan mengalami perubahan-perubahan signifikan, karena <b>Guido van Rossum</b> (pencipta Python) telah memutuskan untuk mengganti
Python 2.x dengan cara yang tepat, dan versi terbaru dari Python 2.x hanya akan
mengalami sedikit perbaikan. Sebaliknya Python 3.x mengalami perkembangan yang
signifikan, seperti:</div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->-<span style="font-size: 7pt;">
</span><!--[endif]-->dukungan <i>Unicode</i>
yang lebih baik </div>
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<!--[if !supportLists]-->-<span style="font-size: 7pt;">
</span><!--[endif]-->bagian inti bahasa pemrograman ini menjadi lebih mudah
untuk dipahami oleh sahabat yang baru belajar, dan lebih konsisten dengan
bagian lain dari bahasa pemrograman ini</div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->-<span style="font-size: 7pt;">
</span><!--[endif]-->mengurangi kelemahan-kelemahan dari versi sebelumnya
sehingga penggunaan<i> memory</i> menjadi
lebih efisien</div>
<div class="MsoNormal" style="margin: 0in 0in 12pt 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->-<span style="font-size: 7pt;">
</span><!--[endif]-->standar <i>library</i>
terbaru juga hanya tersedia di Python 3.x</div>
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<b>Sekarang, versi mana yang sebaiknya dipilih?<o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Memilih
versi mana yang sebaiknya digunakan akan sangat tergantung dari ‘apa yang
hendak sahabat kerjakan dengan Python?’. Jika sahabat mengerti dengan baik apa
yang hendak sahabat lakukan, dan mengenal Python 3.x dengan baik maka memilih
Python 3.x sangatlah tepat. Perlu diingat bahwa dukungan terhadap Python 3.x
masih sedikit. Namun sebagai bahasa pemrograman, Python 3.x telah siap untuk
digunakan. </div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Secara
<i>default</i>, Linux dan Macs masih menggunakan
Python 2.x begitu pula dengan dukungan dari perangkat lunak lainnya yang
umumnya belum dapat memahami (belum mendukung modul-modul) Python versi 3.x.
Programer, pada umumnya, masih menggunakan versi 2.x. Oleh karena itu jika
sahabat akan menggunakan Python untuk berhubungan dengan perangkat lunak
lainnya maka sebaiknya sahabat menggunakan versi 2.x.</div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Python
3.x tetap merupakan pilihan yang bagus. Jika sahabat telah terlanjur
menggunakan versi ini, namun terpaksa saudara harus merubah (<i>convert</i>) <i>source</i> ke dalam versi 2.x, misalnya untuk alasan <i>compatibility</i>, maka sahabat tidak perlu
terlalu khawatir. Sudah cukup banyak programmer yang mengembangkan perangkat
lunak untuk mengubah <i>source code</i>
sahabat yang ditulis dalam versi 3.x menjadi versi 2.x. Dokumentesi pada <i>web</i> maupun sebagian <i>textbook</i> masih menggunakan versi 2.x, tetapi tutorial terbaru
umumnya sudah menggunakan versi 3.x.</div>
<div class="MsoNormal" style="margin-bottom: 12pt; text-align: justify;">
Modul-modul
popular yang belum cocok (<i>compatible</i>)
dengan Python 3 misalnya: Twisted, Gevent, Django, dan PIL. Modul-modul
tersebut sedang dalam tahap pengembangan akhir, sehingga tidak lama lagi sudah dapat
digunakan. Dalam hal GUI Python 3 juga telah memiliki dukungan dan kemajuan
yang sangat pesat, dan untuk keterangan lebih jelasnnya dapat sahabat baca <a href="http://wiki.python.org/moin/Python2orPython3">disini</a>.</div>
<div class="MsoNormal" style="margin-bottom: 12.0pt;">
<o:p> </o:p><b style="text-indent: 0in;">Download yang mana?</b></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Setelah
memutuskan versi Python yang akan dipilih, sahabat mungkin akan langsung
berpikir untuk segera mengunduh <i>installer</i>.
Tidak seperti Linux dan Macs, <i>default</i>
Windows tidak memiliki Python. Untuk mengunduh <i>installer</i>, sahabat dapat melakukannya dengan mengunjungi situs
resminya <a href="http://python.org/download/">di sini</a>,
dan saudara akan menemukan halaman seperti pada gambar berikut:</div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
<br /></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ2jCLKa3xZV-jyL120enSKILuw2aGjbkewa3hXWKuaUcSPLqOjGqYjzVj-FL3xMcANN9zRXj1wfme1co16mFGqslzge0DwwxOMeEs4BrNN1AUcJsOjTc2vEm624yY6KQDH130yKT8kZOp/s1600/Gambar+3+-+Python+download+page.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="330" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ2jCLKa3xZV-jyL120enSKILuw2aGjbkewa3hXWKuaUcSPLqOjGqYjzVj-FL3xMcANN9zRXj1wfme1co16mFGqslzge0DwwxOMeEs4BrNN1AUcJsOjTc2vEm624yY6KQDH130yKT8kZOp/s640/Gambar+3+-+Python+download+page.jpg" width="640" /></a></div>
<div class="MsoNormal" style="text-align: center; text-indent: 27pt;">
<o:p> </o:p><span style="text-align: center; text-indent: 0in;">Gambar 3. Halaman </span><i style="text-align: center; text-indent: 0in;">download</i><span style="text-align: center; text-indent: 0in;"> Python</span></div>
<div class="MsoNormal" style="text-align: center; text-indent: 27pt;">
<span style="text-align: center; text-indent: 0in;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 27pt;">
Sebelum
mendownload, mungkin sahabat akan bertanya lagi: “yang mana yang harus saya
unduh? Di situ terdapat dua tipe <i>installer</i>
untuk Windows.” Jika sahabat menggunakan windows 32 bit maka harus mengunduh <i>installer</i> yang paling atas, ‘Python
x.x.x Windows Installer’. Jika sahabat menggunakan windows 64 bit maka sahabat
perlu mengunduh <i>installer</i> yang kedua,
‘Python x.x.x Windows X86-64 MSI Installer’. Berdasarkan yang saya ketahui,
sahabat bisa meng-<i>install</i> Python 32
bit pada Windows 64 bit, tetapi tidak sebaliknya, sahabat tidak dapat meng-<i>install</i> versi 64 bit pada Windows 32
bit.</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<br /></div>
<h2>
<!--[if !supportLists]-->1.3.<span style="font-size: 7pt; font-weight: normal;">
</span><!--[endif]-->Meng-install Phyton</h2>
<div class="MsoNormal" style="margin-bottom: 12pt; text-align: justify; text-indent: 27pt;">
Selesai
mengunduh?? Mari kita lanjutkan dengan melakukan instalasi. Lakukan klik ganda
pada hasil unduhan kita tadi, dan jendela instalasi akan muncul. Ikutilah
setiap tahapannya, seperti meng-<i>install</i>
program sederhana lainnya. Jika sudah, coba lihat <i>Start Menu</i>, sahabat akan menemukan beberapa menu baru, salah
satunya adalah IDLE (Python GUI). Pilih menu tersebut untuk jalankan Python. </div>
<div class="MsoNormal" style="margin-bottom: 12pt; text-align: justify; text-indent: 27pt;">
Seperti yang
telah diketahui sebelumnya, Python adalah <i>interpreter</i>,
sehingga sahabat cukup menuliskan <i>code</i>
yang diinginkan pada jendela IDLE tadi, kemudian tekan/pilih run. Jika sahabat
ini membuat <i>script</i>, sahabat dapat
memilih <i>File</i> <span style="font-family: Wingdings; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">à</span> <i>New Window</i>, hingga muncul jendela kerja baru. Isi dengan <i>code</i> yang sahabat inginkan, kemudian
tekan F5 atau pilih <i>Run</i> <span style="font-family: Wingdings; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">à</span>
<i>Run Module</i>. Dan sahabat akan diminta
untuk menyimpan (<i>save</i>) terlebih
dahulu. Simpanlah file <i>script</i>
tersebut dengan nama yang saudara inginkan dengan tambahan ekstensi “.py”, misal
“file.py”. Setelah disimpan, program tersbut akan langsung dijalankan dan
keluaran dari <i>source code</i> tersebut akan
ditampilkan pada jendela IDLE tadi. </div>
<div class="MsoNormal" style="margin-bottom: 12pt; text-align: justify; text-indent: 27pt;">
Untuk
program-program pendek dan sederhana, banyak programmer yang lebih suka
menjalankan Python melalui <i>command prompt</i>.
Untuk dapat menjalankan Python melalui kita perlu memastikan bahwa <i>runtime</i> telah di-<i>setting</i> secara benar. Untuk memastikan PATH pada <i>System Properties</i> telah di ditambahkan
dengan <i>path directory</i> dari Python.
Berikut langkah-langkah untuk menambahkan:</div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->1.<span style="font-size: 7pt;">
</span><!--[endif]-->Masuk ke jendela <i>Advance
System Setting</i> melalui <i>Properties</i>
pada <i>My Computer</i> atau melalui <i>System</i> pada <i>Control Panel</i>. </div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->2.<span style="font-size: 7pt;">
</span><!--[endif]-->Setelah jendela <i>System
Properties</i> terbuka, masuk pada tab A<i>dvance</i>,
dan klik pada tombol ‘<i>Environment Variables</i>…’ hingga muncul tab <i>Environment Variable</i>.</div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->3.<span style="font-size: 7pt;">
</span><!--[endif]-->Perhatikan tabel kedua
yang berjudul <i>System Variables</i>, <i>scroll</i> ke bawah dan carilah variabel
bernama <b>Path</b> dan lakukan klik ganda
pada variabel <b>Path</b> itu, atau klik
sekali dan pilih <i>edit</i>.</div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->4.<span style="font-size: 7pt;">
</span><!--[endif]-->HATI-HATI melakukan
langkah ini, karena yang akan kita lakukan adalah MENAMBAHKAN <i>path</i> dari tempat kita meng-<i>install</i> Python (misalnya: <b>C:\Program Files\Python27</b>) ke dalam <i>Variable Values</i> dengan menggunakan tanda
<i>semicolon</i> (<b>;</b>) sebagai pemisah dengan <i>path</i>
<i>software</i> yang lain. INGAT, JANGAN
MENGHAPUS/MENGGANTI <i>Variable Values</i> YANG
SUDAH ADA. Jika sahabat tidak sengaja menghapus atau mengubah <i>Variable Values</i> sebelumnya, maka sahabat
tinggal menekan tombol <i>cancel</i> dan
ulangi langkah-langkah diatas. Cara sederhananya sahabat cukup melakukan klik
pada kolom masukan <i>Variable Values</i>,
kemudian menekan tombol <i>End</i> pada <i>keyboard</i>, sehingga membawa sahabat pada
bagian akhir. Sahabat tinggal menambahkan tanda <b>;</b> barulah kemudian sahabat memasukan <i>path</i> (alamat <i>folder</i>)
tempat sahabat meng-<i>install</i> Python.
Contohnya “… <b>;C:\Program Files\Python27</b>”</div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;">
<!--[if !supportLists]-->5.<span style="font-size: 7pt;">
</span><!--[endif]-->Jika sahabat telah
menambahkan <i>path</i> tersebut, sahabat
tinggal menekan tombol <b>Ok</b> pada
jendela-jendela yang tadi telah dibuka, kemudian membuka <i>Command Prompt</i> untuk menguji dan mulai menggunakan Python.</div>
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Untuk mengetahui bahwa Python telah terhubung maka
sahabat cukup mengetikkan <b>python</b>
pada <i>Command Prompt</i>, kemudian tekan <i>enter</i>. Jika sahabat <i>Command Prompt</i> telah menampilkan versi Python yang sahabat gunakan
dan muncul ‘<b>>>></b>’ berarti
sahabat telah berhasil dan Python siap diajak bermain. Untuk keluar dari Python
dan menggunakan <i>Command Prompt</i> yang biasa
sahabat cukup menggunakan perintah <b>quit()</b>.<o:p></o:p></div>
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***<o:p></o:p></div>
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<br /></div>
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<h1 style="margin-left: 0in; mso-list: none;">
BIBLIOGRAPHY</h1>
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<br /></div>
<div class="MsoBibliography" style="margin-left: 27pt; text-align: justify; text-indent: -27pt;">
Downey, A. (2012). <i>Think Python: How to Think Like
a Computer Scientist</i> (Version 2.0.1 ed.). Needham, Massachusetts: Green Tea
Press.<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 27pt; text-align: justify; text-indent: -27pt;">
<i>Guide to installing Python in Windows Vista</i>. (n.d.). Retrieved August 24, 2012, from Neural Wiki:
<a href="http://www.neuralwiki.org/index.php?title=Guide_to_installing_Python_in_Windows_Vista">http://www.neuralwiki.org/index.php?title=Guide_to_installing_Python_in_Windows_Vista</a>
<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 27pt; text-align: justify; text-indent: -27pt;">
ismailsunni. (2012, February 28). <i>Hello, Python</i>.
Retrieved August 24, 2012, from Mathlete's Code: <a href="http://codemath.wordpress.com/2012/02/28/hello-python/">http://codemath.wordpress.com/2012/02/28/hello-python/</a>
<o:p></o:p></div>
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Python
official website. <a href="http://python.org/">http://python.org</a> </div>
skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com2tag:blogger.com,1999:blog-9034572127535224290.post-74099618197837834972012-08-20T12:05:00.000-07:002014-07-22T08:52:25.411-07:00MENGHUBUNGKAN DAN MENGGUNAKAN LCD SEBAGAI PERIPHERAL PADA MIKROKONTROLER AVR DENGAN AVR STUDIO 5<br />
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<h2>
1.1.<span style="font-size: 7pt; font-weight: normal;">
</span>PENGENALAN LCD</h2>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8-eTbbDgz6qtDoF4Afh3m9VDWU1GZcW-i7vB25bmX9ev6SK-kFGrTtSTuZFk3Os1AR1GVnP8wR15PZZciGnlzVEYWWS-1EbY42qC7NtWGnAA7gq45NCeDeoyCwtoewplAnCI1z7z4Sf6u/s1600/Gambar+1+-+LCD.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8-eTbbDgz6qtDoF4Afh3m9VDWU1GZcW-i7vB25bmX9ev6SK-kFGrTtSTuZFk3Os1AR1GVnP8wR15PZZciGnlzVEYWWS-1EbY42qC7NtWGnAA7gq45NCeDeoyCwtoewplAnCI1z7z4Sf6u/s320/Gambar+1+-+LCD.jpg" height="127" width="320" /></a></div>
<span style="text-indent: 0in;">Gambar 1. </span><i style="text-indent: 0in;">Liquid Crystal Display</i></div>
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<span style="font-size: 10pt; line-height: 19.200000762939453px;">(a) <i>Graphical</i> LCD; (b) <i>Character</i> LCD</span></div>
<br />
<div style="text-align: justify;">
<span style="text-indent: 0in;">LCD merupakan singkatan dari</span><span style="text-indent: 0in;"> </span><i style="text-indent: 0in;">Liquid Crystal Display</i><span style="text-indent: 0in;">. LCD merupakan alat atau komponen yang digunakan untuk menampilkan berbagai hal secara visual. Ada banyak jenis LCD, namun yang secara umum yang digunakan dalam dunia robotika atau mikrokontroler dapat dikelompokan dalam dua jenis yaitu,</span><span style="text-indent: 0in;"> </span><i style="text-indent: 0in;">character</i><span style="text-indent: 0in;"> </span><span style="text-indent: 0in;">LCD dan</span><span style="text-indent: 0in;"> </span><i style="text-indent: 0in;">graphical</i><span style="text-indent: 0in;"> </span><span style="text-indent: 0in;">LCD. Pada tulisan ini akan yang akan dibahas adalah jenis LCD yang lebih sederhana yaitu</span><span style="text-indent: 0in;"> </span><i style="text-indent: 0in;">character</i><span style="text-indent: 0in;"> </span><span style="text-indent: 0in;">LCD.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbKBQMzf-nKvE7781GORYr9RgpI-IIpHDP7x6funSFeT8zOMh0tf3fOm75-p6CDxYvFNVyw9LXJhzC3JMGTL7K_ebkQywHYVoKWw0vluFFfUc5Ciq4m3Useh3AqRhrMmuyUmKARdo7Zmvn/s1600/Gambar+2+-JHD162A.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbKBQMzf-nKvE7781GORYr9RgpI-IIpHDP7x6funSFeT8zOMh0tf3fOm75-p6CDxYvFNVyw9LXJhzC3JMGTL7K_ebkQywHYVoKWw0vluFFfUc5Ciq4m3Useh3AqRhrMmuyUmKARdo7Zmvn/s1600/Gambar+2+-JHD162A.jpg" /></a></div>
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<span style="text-indent: 27pt;">Gambar 2. LCD JHD
162A</span></div>
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Hitachi HD44780 adalah salah satu seri <i>character</i> LCD yang umum digunakan dalam
dunia mikrokontroler. LCD ini mampu menampilkan karakter dalam ukuran 2 baris
yang masing-masing baris terdiri dari 16 kolom. Namun yang akan digunakan dalam
arttikel ini adalah LCD seri JHD 162A. LCD seri JHD 162A ini memiliki bentuk
yang hampir sama dan memiliki desain yang kompetibel dengan seri HD44780,
sehingga dapat berjalan dengan <i>code</i>
yang yang sama. Kedua LCD ini memiliki konfigurasi pin yang sama seperti dapat
dilihat pada table 1:</div>
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Tabel
1. Konfigurasi pin LCD</div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 5.4pt; mso-border-alt: solid black .5pt; mso-border-insideh: .5pt solid black; mso-border-insidev: .5pt solid black; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 97%px;">
<tbody>
<tr>
<td style="border: solid black 1.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" valign="top" width="7%"><div class="MsoNormal" style="text-indent: 0in;">
No.<br />
PIN</div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
NAMA</div>
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FUNGSI</div>
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</tr>
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<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
1</div>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
V<sub>SS</sub></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<i>Ground</i> (referensi tegangan)</div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
2</div>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
V<sub>CC</sub></div>
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<i>Power</i> (<i>Positive voltage</i>), +5 Volt</div>
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<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
3</div>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
V<sub>EE</sub></div>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<i>Contrast Voltage</i> (tegangan pengatur
kontras)</div>
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</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
4</div>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
RS</div>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<i>Register Select</i> (memilih register): </div>
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0
= <i>Instruction Register</i>
(mengaktifkan register instruksi)</div>
<div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
1
= <i>Data Register</i> (mengaktifkan
register penerima data)</div>
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</tr>
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<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
5</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
R/W</div>
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<i>Read</i>/<i>Write</i>:<br />
0 = <i>Write mode</i> (LCD bekerja dalam
modus menulis)</div>
<div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
1
= <i>Read Mode</i> (LCD bekerja pada modus
data LCD bisa dibaca)</div>
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<div style="text-align: justify;">
Umumnya,
read mode jarang digunakan sehingga sebagain orang hanya menghubungkan PIN
ini pada <i>ground</i> (0 = modus menulis)</div>
</div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
6</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
E</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<i>Enable</i>:</div>
<div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
0
= Mulai menampung (<i>save</i>/<i>latch</i>) data karakter pada LCD</div>
<div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
1
= <i>disable</i> / me-nonaktifkan</div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
7</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB0</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #00b050;">Data
Bit 0 (LSB)<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
8</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB1</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #00b050;">Data
Bit 1<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
9</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB2</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #00b050;">Data
Bit 2<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
10</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB3</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #00b050;">Data
Bit 3<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
11</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB4</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #0070c0;">Data Bit 1</span> / <span style="color: #00b050;">Data
Bit 4</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
12</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB5</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #0070c0;">Data Bit 2</span> / <span style="color: #00b050;">Data
Bit 5</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
13</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB6</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #0070c0;">Data Bit 3</span> / <span style="color: #00b050;">Data
Bit 6</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
14</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
DB7</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<span style="color: #0070c0;">Data Bit 4</span> / <span style="color: #00b050;">Data Bit
7 (MSB)</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
15</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
BPL</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<i>Back Plane Light</i> ( tegangan untuk <i>backlight</i>), +5 Volt atau lebih rendah</div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 7.44%;" width="7%"><div align="center" class="MsoNormal" style="margin-bottom: 12pt; text-align: center; text-indent: 0in;">
16</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 11.7%;" width="11%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
GND</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 80.86%;" valign="bottom" width="80%"><div align="left" class="MsoNormal" style="margin-bottom: 12pt; text-indent: 0in;">
<i>Ground<o:p></o:p></i></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<br /></div>
<h2>
</h2>
<div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<br /></div>
</div>
<h2>
1.2.<span style="font-size: 7pt; font-weight: normal;"> </span>Menghubungkan LCD</h2>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Kedua
seri <i>character</i> LCD yang disebutkan
sebelumnya, dapat beroperasi dengan mode 8 bit maupun mode 4 bit. Mode 8 bit
akan menghasilkan proses yang lebih cepat, tetapi memerlukan 8 pin koneksi data
pada mikrokontroler. Sedangakan mode 4 bit lebih lambat dibandingkan mode 8
bit, tetapi hanya memerlukan 4 pin untuk mengirimkan data dari mikrokontroler
(koneksi data belum termasuk koneksi pengendalian). Namun umumnya kecepatan
pengolahan data mode 4 bit sudah cukup memenuhi kebutuhan dan lebih umum
digunakan oleh para pecinta mikrokontroler. Oleh karena pada tulisan ini kita
akan belajar menghubungkan mikrokontroler dan LCD JHD 162A dengan mode 4 pin.</div>
</div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicXZPJbnDH8QkocQzKtQnfTH6vZW8X4XSrDmH9AqxW51KrqZnH2m1PMlncYlHH16N6tkAqYPKIAdH83X4HaHXhAFWbd251N8siyG3DyDLzuDhoc444LYKs1QKaNek6i7w8xz7bU3wGm0kw/s1600/Gambar+3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicXZPJbnDH8QkocQzKtQnfTH6vZW8X4XSrDmH9AqxW51KrqZnH2m1PMlncYlHH16N6tkAqYPKIAdH83X4HaHXhAFWbd251N8siyG3DyDLzuDhoc444LYKs1QKaNek6i7w8xz7bU3wGm0kw/s640/Gambar+3.jpg" height="449" width="640" /></a></div>
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 27.0pt;">
Gambar 3. Skema penggunaan LCD dengan modus
4 bit.<br />
<br />
<br /></div>
<h2>
1.3.<span style="font-size: 7pt; font-weight: normal;">
</span>Menggunakan LCD</h2>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<div style="text-align: justify;">
Sebelum mulai
menggunakan alat atau komponen elektronik tertentu biasanya kita akan mencoba
untuk mempelajari datasheet dari komponen tersebut, misalnya data sheet dari
LCD <a href="http://www.sparkfun.com/datasheets/LCD/HD44780.pdf">ini</a>.
Tapi untuk menghasilkan proses pembelajaran yang lebih produktif dan efisien,
sahabat tidak perlu melakukan hal tersebut. Saya yakin sahabat suka dengan hal
yang lebih sederhana. <a href="http://homepage.hispeed.ch/peterfleury/">Peter Fleury</a> telah
menyediakan library LCD, yang dapat sahabat unduh di <a href="http://homepage.hispeed.ch/peterfleury/lcdlibrary.zip">sini</a>. Oleh karena
itu sebelum memulai coding dengan AVR Studio 5, sebaiknya sahabat memiliki
mengunduh dan meng-<i>extract</i> library
tersebut. </div>
</div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<div style="text-align: justify;">
Sekarang
kita akan memulai dengan membuka AVR Studio 5 dan memulai <i>create new project</i>. Setelah terbuka, pada panel disebelah kanan,
sahabat akan menemukan jendela <i>Solution
Explorer</i>. Lakukan klik kanan pada nama <i>project</i>
di jendela tersebut. kemudian pilih <i>Go to</i>
<span style="font-family: Wingdings; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">à</span>
<i>Add</i> dan kemudian pilih <i>Existing Item</i>. Jendela pencarian akan
muncul, dan sahabat tinggal memilih (<i>Add</i>)
file <i>lcd.c</i> dan kemudian ulangi
langkah diatas untuk memilih file <i>lcd.h</i>.
Akhirnya kita dapat melihat kedua file (file c dan file <i>header</i> dari <i>library</i> LCD)
tertera pada <i>project</i> kita. </div>
</div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8ESvbW8Ljc4KVHRYhC1TCObvQBdwSdwpm2NbN8fZmz__19kGXlFvUeG14rNTuKLMjOUVOwxv0tDXEIWFSxJvz4EiBOBBzG9xFykQCmrxdvh2C15hRS4lJ6yB1dqWJJS_u3-YvLro6SqZq/s1600/Gambar+4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8ESvbW8Ljc4KVHRYhC1TCObvQBdwSdwpm2NbN8fZmz__19kGXlFvUeG14rNTuKLMjOUVOwxv0tDXEIWFSxJvz4EiBOBBzG9xFykQCmrxdvh2C15hRS4lJ6yB1dqWJJS_u3-YvLro6SqZq/s1600/Gambar+4.jpg" /></a></div>
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 12.0pt; text-align: center; text-indent: 0in;">
Gambar 4. Menambahkan library LCD pada <i>project</i> di AVR Studio 5</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Setelah kita menambahkan library
LCD pada project kita, mari lanjutkan dengan mengatur konfigurasi yang sesuai
untuk library tersebut, dengan mengikuti langkah-langkah berikut ini: </div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span>Lakukan double click pada bagian ‘<i>lcd.h</i>’ (pada jendela Solution Explorer), sehingga akan memunculkan
tab ‘<i>lcd.h</i>’. Selanjutnya lakukan
scroll ke bawah secara perlahan agar kita tidak melewatkan hal-hal yang
penting. </div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span>Pada bagian awal kita akan menemui beberapa teks
komentar yang mendeskripsikan tentang <i>library</i>
tersebut.</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span>Jika kita melakukan <i>scroll</i>
ke bawah lagi maka kita akan menemukan bahwa baris yang mendefinisikan nilai
XTAL (atau F_CPU). Sesuaikan nilainya dengan nilai <i>clock</i> (F_CPU) yang kita gunakan pada mikrokontroler. Jika nilai ini
tidak sesuai maka kita akan mendapatkan waktu <i>delay</i> yang tidak sesuai juga.</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span><i>Scroll</i> lagi ke
bawah dan kita akan menemukan baris yang mendefinisikan LCD_IO_MODE. Seperti
telah dijelaskan pada deskripsi di bagian awal, LCD_IO_MODE = 0 berarti LCD
dalam modus <i>memory mapped</i>. Sedangakan
untuk LCD_IO_MODE = 1 berarti LCD dalam modus 4 bit. Pastikan agar LCD_IO_MODE
di set dengan nilai 1 (modus 4 bit). Perlu diingat bahwa <i>library</i> ini tidak mendukung modus 8 bit.</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span>Setelah bagian LCD_IO_MODE maka kita akan menemukan
bagian penting lainnya, yaitu pendefinisian <i>port</i>/<i>pin</i> pada mikrokontroler yang telah
dihubungkan dengan LCD. Sesuaikan port dan pin yang anda gunakan. Umumnya,
DB4,…,DB7 pada LCD dihubungkan dengan pin D4 hingga D7 pada mikrokontroler.
Sedangkan 3 pin pengendali LCD (RE, R/W, E) bebas sesuai keiinginan kita. Sebenarnya,
kita bebas mengatur pin yang digunakan, yang terpenting adalah kita
mendefinisikan pin-pin tersebut pada bagian ini sesuai dengan keadaan yang
sebenarnya.</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span>Sahabat telah selesai melakukan proses pengaturan
pendefinisian atau pengaturan konfigurasi. Jangan lupa untuk menyimpan (<i>save</i>) semua <i>setting</i> yang telah sahabat lakukan dalam <i>lcd.h</i> ini. </div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span>Jika kita tetap melakukan <i>scroll</i> lebih lanjut lagi maka kita akan menemukan rangkaian daftar
perintah pada LCD yang dapat dijalankan dengan meng-<i>input</i>-kan perintah tersebut pada fungsi <i>lcd_command()</i>. </div>
</div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; margin-left: .25in; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;"> </span>Selanjutnya kita juga akan menemukan rangkaian daftar
fungsi bersama deskripsinya, yang di definisikan melalui library ini.
Fungsi-fungsi tersebut antara lain <i>lcd_init()</i>,
<i>lcd_clrscr()</i>, <i>lcd_home()</i>, <i>lcd_gotoxy()</i>,
<i>lcd_putc()</i>, <i>lcd_puts()</i>, <i>lcd_puts_p()</i>,
<i>lcd_command()</i>, <i>lcd_data()</i> dan <i>lcd_puts_P()</i>.
Their description is attached alongwith their declaration. </div>
</div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 0in;">
<div style="text-align: justify;">
Terakhir, jangan
lupa untuk memasukan (<i>#include</i>) “<i>lcd.h</i>” pada bagian header file c <i>project</i> kita. Sekarang kita sudah siap
untuk melakukan <i>coding</i> untuk
menampilkan karakter yang kita inginkan pada LCD. </div>
</div>
<div class="MsoNormal" style="text-indent: 0in;">
<b>Coding<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<div style="text-align: justify;">
Mari kita
coba menampilkan karakter yang sederhana, sekaligus untuk memeriksa apakah kita
telah berhasil menghubungkan LCD dan mikrokontroler kita. Sahabat bisa
menggunakan code berikut ini:</div>
</div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 12.0pt; text-align: center; text-indent: 0in;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs4luAdZjKVbTgYEOyVvboiuTwRk2n5e8RKDJBLgamUtlJFk07ZiD1i-SuygEFOeQS-9YW3vra3uv9SjspXTss2OO-CepV1rQEOPNnHC8qbZFm0YDvCX-EZEwBsjP8hD6rj-B7FgoJz6X0/s1600/Gambar+5+-+c+code+karakter+sederhana.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs4luAdZjKVbTgYEOyVvboiuTwRk2n5e8RKDJBLgamUtlJFk07ZiD1i-SuygEFOeQS-9YW3vra3uv9SjspXTss2OO-CepV1rQEOPNnHC8qbZFm0YDvCX-EZEwBsjP8hD6rj-B7FgoJz6X0/s640/Gambar+5+-+c+code+karakter+sederhana.jpg" height="327" width="640" /></a></div>
Gambar 5. Contoh c <i>code</i>
untuk menampilkan karakter sederhana pada LCD</div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<div style="text-align: justify;">
Jika sudah
selesai mengetik code diatas, lakukan compile dan build untuk menghasilkan file
hex. Lakukan burning/programming/flashing file tersebut ke dalam mikrokontroler
sahabat yang sudah terhubung dengan LCD dan lihat apa yang terjadi dengan LCD
sahabat. Jika sahabat telah melihat tulisan “Hallo Sahabat” dan “Sky-Institute”
pada baris pertama dan baris kedua maka saudara telah berhasil menghubungkan
dan menggunakan LCD. </div>
</div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<div style="text-align: justify;">
Sekarang
mari kita pelajari sesuatu yang lebih, sekaligus mematangkan kemampuan sahabat
dalam menggunakan LCD karakter ini.</div>
</div>
<h3>
1.3.1.<span style="font-size: 7pt; font-weight: normal;"> </span>Menampilkan
karakter/<i>string</i> dinamis</h3>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<div style="text-align: justify;">
Pada bagian
ini kita akan melihat contoh bagaimana menampilkan karakter yang
dinamis/bergerak pada LCD kita. Mempelajari bagian ini akan membantu kita untuk
lebih mengeksplore dan mengenal <i>library</i>
LCD yang kita tambahkan diatas. Bagian ini juga akan membuat kemampuan sahabat
semakin bertambah, dan saya yakin hal ini akan memberikan kesenangan dan
kepuasan bagi sahabat yang sedang mempelajari pengunaan LCD. </div>
</div>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 27.0pt;">
<div style="text-align: justify;">
Kali ini
kita akam menampilkan tulisan atau karakter yang akan bergerak. Sebagai tips:
gunakanlah perintah/fungsi <i>lcd_command</i>()
yang telah kita lihat sebelumnya, misalnya <i>lcd_command</i>(LCD_MOVE_DISP_RIGHT)
untuk menggerakan karakter ke kanan, <i>lcd_command</i>(LCD_MOVE_DISP_LEFT),
dan lain-lain. Kemudian coba buat agar tulisan tersebut dapat berputar
bergantian antara baris satu dan baris kedua pada LCD. Sahabat bisa mempelajari
lebih jauh menggunakan <i>code</i> berikut
ini:</div>
</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFeRNFWhZcdqs8_03dA1F44fuJvu-x8ijov2wYz3gIgBDUIeDh6aToYizdY-qDFvHedSE576dqpF726qC0if53lEs-W2b9zIbaK-XYWpQcHo036Zq-61gGVapv15Ub9Gqeen0SnH0apw_g/s1600/Gambar+6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFeRNFWhZcdqs8_03dA1F44fuJvu-x8ijov2wYz3gIgBDUIeDh6aToYizdY-qDFvHedSE576dqpF726qC0if53lEs-W2b9zIbaK-XYWpQcHo036Zq-61gGVapv15Ub9Gqeen0SnH0apw_g/s1600/Gambar+6.jpg" /></a></div>
<br /></div>
<div align="right" class="MsoNormal" style="text-align: right; text-indent: 0in;">
<span style="font-size: 10.0pt; line-height: 150%; mso-bidi-font-size: 12.0pt;">Sumber: <a href="http://www.avrfreaks.net/index.php?name=PNphpBB2&file=viewtopic&t=81823">http://www.avrfreaks.net/index.php?name=PNphpBB2&file=viewtopic&t=81823</a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
Gambar 6. Contoh c <i>code</i>
untuk menampilkan karakter dinamis</div>
<h3>
1.3.2.<span style="font-size: 7pt; font-weight: normal;"> </span>Menampilkan
nilai atau angka (<i>integer</i>, <i>float</i>):</h3>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Seperti namanya LCD karakter,
maka fungsinya pun untuk menampilkan karakter. Namun bagaimana jika sahabat
ingin menampilkan data <i>integer</i>, <i>float</i> atau yang lain? Apakah hal
tersebut dapat dilakukan? Pada dasarnya yang dapat kita <i>display</i> adalah grafik ataupun karakter. Sedangkan integer dan
proses aritmatik hanya bisa terjadi didalam otak. Angka merupakan merupakan
representasi karakter dari sebuah data <i>integer</i>,
<i>float</i>, dan lain-lain. Oleh karena itu
kita dapat menampilkan data <i>integer</i>
ataupun hasil operasi aritmatika lainnya, tetapi kita perlu
‘merubah’/merepresentasikan dalam bentuk data karakter (<i>string</i>).</div>
</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Untuk mengubah data integer
menjadi data string kita dapat menggunakan perintah/fungsi <i>itoa</i>(<i>integer_yg_ingin_diubah</i>,
<i>representasi_string_nya</i>, <i>basis</i>). Dengan fungsi tersebut kita
dapat ‘mengubah’ data integer menjadi data karakter sesuai basis yang
diinginkan. Misalnya jika kita ingin mengubah data <i>integer</i> 14 menjadi data <i>string</i>
dalam bentuk biner maka basis kita isi dengan 2. Dari pada berpanjang lebar,
mari kita lakukan percobaan dengan <i>code</i>
berikut ini:</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9iHtOYdxrOeGRQRRfc8M6QR0LmFKDtplaHhtM8xY8CfNGg7xp2917gJwq1J_N35S9ZxLkjmcv9K74GyC-eeQoT4EayjlwZpMcXpiCjjjrKImKJKYcvGkFh_1zwCr2yqoy6jX95nPkeN1N/s1600/Gambar+7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9iHtOYdxrOeGRQRRfc8M6QR0LmFKDtplaHhtM8xY8CfNGg7xp2917gJwq1J_N35S9ZxLkjmcv9K74GyC-eeQoT4EayjlwZpMcXpiCjjjrKImKJKYcvGkFh_1zwCr2yqoy6jX95nPkeN1N/s1600/Gambar+7.jpg" /></a></div>
</div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<span style="text-indent: 0in;">Gambar
7. C </span><i style="text-indent: 0in;">code</i><span style="text-indent: 0in;"> untuk menampilkan data </span><i style="text-indent: 0in;">integer</i></div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<br />
<div style="text-align: justify;">
Secara umum, kita tidak
disarankan untuk menggunakan perhitungan decimal (<i>float number</i>) dalam melakukan pemrograman mikrokontroler. Hal ini
disebabkan karena umumnya inti otak dari mikrokontroler tidak dilengkapi dengan
kemampuan untuk melakukan operasi aritmatik dengan bilangan decimal. Yang dapat
dilakukan oleh otak dari mikrokontroler adalah melakukan operasi aritmatik.
Namun secara <i>engineer</i> hal itu dapat
dilakukan dengan mensimulasi (<i>emulate</i>)
operasi aritmatik tersebut pada perangkat lunaknya. </div>
</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Jika sahabat melakukan operasi
aritmatik sederhana dan selalu menghasilkan bilangan bulat (<i>integer</i>) maka sahabat tidak perlu
khawatir karena mikrokontroler dapat melakukannya dengan mudah. Tetapi jika
pecahan atau bilangan desimal (<i>float</i>)
tidak dapat dihindari maka sahabat perlu menggunakan perintah <i>sprintf</i>(). Seperti yang telah disebutkan
diatas bahwa untuk melakukan operasi aritmatik bilangan decimal maka kita perlu
menambahkan semacam emulator pada mikrokontroler kita. Fungsi <i>sprintf</i>() umum digunakan, tetapi membutuhkan
waktu dan memori yang lebih banyak dibandingkan operasi aritmatik sederhana.
Oleh karena itu sedapat mungkin sabahat menggunakan perhitungan yang sederhana.</div>
</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Terkadang kita tidak dapat
menghindar dari operasi aritmatik bilangan desimal. Pilihan lain adalah dengan
menggunakan perintah/fungsi seperti <i>dtostre</i>()
atau <i>dtostrf</i>(), karen fungsi-fungsi
tersebut memiliki <i>library</i> yang lebih
sederhana dan ringan dibandingkan perintah <i>sprintf</i>().
Atau kita juga dapat menggunakan perintah <i>rprintfFloat</i>(<i>jmlhdigit</i>, <i>double_or_float</i>) yang terdapat pada library AVR (<i>rprintf.h</i>). </div>
</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Sekarang mari kita coba
menampilkan data float ke dalam LCD, misalnya data tekanan udara. </div>
</div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 12.0pt; text-align: center; text-indent: 0in;">
<div class="separator" style="clear: both; text-align: center;">
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Gambar 8. C <i>code</i>
untuk menampilkan data <i>float</i>/<i>double</i></div>
<div class="MsoNormal" style="text-indent: 0in;">
<div style="text-align: justify;">
Setelah sahabat memprogram
mikrokontroler sahabat dengan <i>code</i>
diatas, apakah yang terjadi? Apakah yang muncul di LCD hanya ‘tanda tanya’ (?)
seperti gambar dibawah ini?</div>
</div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 0in;">
<div class="separator" style="clear: both; text-align: center;">
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Gambar
9. <i>Error</i> saat menampikan data <i>float</i> pada LCD</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Masih ingat kan dengan penjelasan
diatas bahwa, untuk melakukan operasi dengan data float, mikrokontroler
membutuhkan ‘emulator’. Nah, kita perlu menjalankan ‘emulator’ tersebut agar
operasi berjalan lancar, dengan cara memberitahukan kepada <i>linker</i> agar menggunakan <i>floating
point library</i>. <i>Library</i> ini
umumnya sudah tersedia dalam <i>software</i>
AVR studio 5, tetapi perlu kita set agar <i>library</i>
tersebut dapat digunakan. <i>Library</i>
yang perlu ditambahkan adalah <b>libprintf_flt.a</b>
dan <b>libm.a</b>, dan kita juga perlu
menambahkan <b>-Wl,-u,vfprintf -lprintf_flt
–lm</b> pada <i>linker option</i> agar <i>library</i> diatas dapat dijalankan dengan
benar. </div>
</div>
<div class="MsoNormal" style="text-indent: 27.0pt;">
<div style="text-align: justify;">
Berikut ini adalah cara
memberitahukan linker pada AVR studio 5 mengenai <i>floating point library</i>:</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>Pada bagian menu klik <i>Project</i> (ALT+F7)</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>Klik Toolchain dan lihat pada bagian <i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial;">AVR/GNU
C Linker</span></i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial;"> dan pilih <i>Libraries</i></span>.</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>Pada bagian <i>Librarier</i>
(-Wl,-l), lakukan klik pada tombol <i>Add</i>,
dan sebuah jendela akan terbuka. Ketikkan (<i>insert</i>)
<b>libprintf_flt.a</b>. Pilih <i>Ok</i> dan ulangi dari tombol <i>Add</i> dan ketikkan <b>libm.a</b>.</div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>Lanjutkan dengan mengklik bagian <i>Miscellaneous</i> pada bagian <i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial;">AVR/GNU C Linker</span></i><span style="background-color: white; background-position: initial initial; background-repeat: initial initial;"> dan ketikkan <b>-Wl,-u,vfprintf -lprintf_flt –lm</b> pada baris input disamping tulisan
<i>Other linker flags</i>.</span></div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<div style="text-align: justify;">
<span style="font-size: 16.0pt; line-height: 150%; mso-bidi-font-size: 12.0pt;">-<span style="font-size: 7pt; line-height: normal;">
</span></span><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; line-height: 150%;">Lakukan <i>save</i>, kemudian <i>rebuild</i>
file C <i>project</i> sahabat.</span><span style="font-size: 16.0pt; line-height: 150%; mso-bidi-font-size: 12.0pt;"><o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="text-indent: 0in;">
<div style="text-align: justify;">
<span style="line-height: 150%; mso-bidi-font-size: 10.0pt;">Program kembali mikrokontroler sahabat dengan file <i>hex</i> yang baru, maka sahabat akan
mendapatkan tampilan pada LCD seperti yang diharapkan. <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="margin-left: 45.0pt; text-indent: -45.0pt;">
<div style="text-align: justify;">
<span style="line-height: 150%; mso-bidi-font-size: 10.0pt;">Catatan: bagi sahabat yang masih menggunakan CV AVR,
sahabat dapat melakukan langkah diatas dengan melakukan klik pada <i>Project</i> </span><span style="font-family: Wingdings; line-height: 150%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">à</span><span style="line-height: 150%; mso-bidi-font-size: 10.0pt;"> <i>Configure</i>, kemudian pada bagian <i>(s)printf
feature</i> ubah statusnya menjadi <b>float,
width, precision</b>. <strong><o:p></o:p></strong></span></div>
</div>
<div class="MsoNormal" style="text-indent: 0in;">
<br /></div>
<div class="MsoNormal" style="text-indent: 0in;">
<b>Kesalahan (<i>error</i>)
yang Sering Terjadi dan Solusinya<o:p></o:p></b></div>
<div class="MsoNormal" style="text-indent: 0in;">
<div style="text-align: justify;">
Saat
menggunakan LCD mungkin sahabat akan menemui beberapa masalah seperti berikut: <o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l0 level1 lfo3; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>tidak ada yang
terlihat di layar<o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l0 level1 lfo3; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>layar tampak
hitam semuanya<o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l0 level1 lfo3; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>hanya tampak
kursor yang berkedip, dan tidak nampak karakter yang diinginkan<o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l0 level1 lfo3; text-indent: -.25in;">
<div style="text-align: justify;">
-<span style="font-size: 7pt;">
</span>tampak karakter
atau simbol yang aneh<o:p></o:p></div>
</div>
<div class="MsoNormal" style="text-indent: 0in;">
<div style="text-align: justify;">
Untuk
masalah-masalah tersebut coba selasaikan dengan langkah-langkah berikut: <o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l1 level1 lfo4; text-indent: -.25in;">
<div style="text-align: justify;">
<span style="font-family: Wingdings; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-no-proof: yes;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Atur resistor variabel (potensiometer) untuk
meningkatkan kontras<o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l1 level1 lfo4; text-indent: -.25in;">
<div style="text-align: justify;">
<span style="font-family: Wingdings; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-no-proof: yes;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Periksa kembali sambungan, mungkin ada koneksi yang
putus atau mengalami short sircuit.<o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l1 level1 lfo4; text-indent: -.25in;">
<div style="text-align: justify;">
<span style="font-family: Wingdings; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-no-proof: yes;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Periksa kembali <i>code</i>
sahabat. Pastikan sahabat telah menggunakan nilai clock (XTAL/F_CPU) yang tepat
pada <i>project</i> utama maupun pada <i>library</i> <i>lcd.h</i>.<o:p></o:p></div>
</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l1 level1 lfo4; text-indent: -.25in;">
<div style="text-align: justify;">
<span style="font-family: Wingdings; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-no-proof: yes;">ü<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Terakhir, jangan lupa bertanya kepada orang lain,
karena mungkin mereka pernah mangalami masalah yang sahabat hadapi, dan mereka
telah berhasil menemukan solusinya. Sahabat juga dapat bertanya di blog ini
melalui jendela <i>comment</i>.<o:p></o:p></div>
</div>
<div class="MsoNormal" style="text-indent: 0in;">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<h1 style="margin-left: 0in; mso-list: none;">
BIBLIOGRAPHY</h1>
<div class="MsoBibliography" style="margin-left: 27.0pt; text-indent: -27.0pt;">
<br /></div>
<div class="MsoBibliography" style="margin-left: 27.0pt; text-indent: -27.0pt;">
<div style="text-align: justify;">
<br />
<div class="MsoBibliography" style="margin-left: 27.0pt; text-indent: -27.0pt;">
dl8dtl. (2006, June 30). <i>How to use sprintf with
floats in AVR STUDIO (winavr compile)</i>. Retrieved August 14, 2012, from
www.avrfreaks.net: <a href="http://www.avrfreaks.net/index.php?name=PNphpBB2&file=viewtopic&t=39892">http://www.avrfreaks.net/index.php?name=PNphpBB2&file=viewtopic&t=39892</a>
<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 27.0pt; text-indent: -27.0pt;">
Motisan, R. (2012, February 8). <i>AVR Studio 5
snprintf / vsnprintf problem with Floats</i>. Retrieved August 14, 2012, from
POCKET MAGIC: Where Technology meets Magic: <a href="http://www.pocketmagic.net/?p=2513">http://www.pocketmagic.net/?p=2513</a>
<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 27.0pt; text-indent: -27.0pt;">
Rudiawan, E. (2012, March 19). <i>ngooprek.com</i>.
Retrieved August 14, 2012, from Belajar AVR – Sensor Interfacing – 13: <a href="http://ngooprek.com/blog/2012/03/19/belajar-avr-sensor-interfacing-13/">http://ngooprek.com/blog/2012/03/19/belajar-avr-sensor-interfacing-13/</a>
<o:p></o:p></div>
<div class="MsoBibliography" style="margin-left: 27.0pt; text-indent: -27.0pt;">
Vitu, M. (2011, June 16). <i>LCD Interfacing with AVR</i>.
Retrieved August 14, 2012, from maxEmbedded: a Guide to Robotics and Embedded
Electronics: <a href="http://maxembedded.wordpress.com/2011/06/16/lcd-interfacing-with-avr/">http://maxembedded.wordpress.com/2011/06/16/lcd-interfacing-with-avr/</a></div>
<div class="MsoBibliography" style="margin-left: 27.0pt; text-indent: -27.0pt;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 150%; text-indent: -27pt;">winavr.scienceprog.com. (2007,
January 19). </span><i style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 150%; text-indent: -27pt;">Using sprintf function for float numbers in AVR-GCC</i><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 150%; text-indent: -27pt;">.
Retrieved August 14, 2012, from AVR-GCC Tutorial WINAVR: </span><a href="http://winavr.scienceprog.com/comment/28" style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 150%; text-indent: -27pt;">http://winavr.scienceprog.com/comment/28</a> </div>
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skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com2tag:blogger.com,1999:blog-9034572127535224290.post-89686593289743650862012-04-21T15:03:00.001-07:002012-08-25T19:47:07.659-07:00ELECTRICITY – GOD’s Finger to Holds the World<br />
<h2 style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 27.0pt; margin-right: 0in; margin-top: 12.0pt; page-break-after: avoid; text-align: justify; text-indent: -27.35pt; text-justify: inter-ideograph;">
1.1. The Beauty of Electricity</h2>
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“<i>Electricity and
magnetism is all around us. We have electric lights, Electric clocks. We have
microphones, calculators, televisions, VCRs, radio, computers. Light itself is
an electromagnetic phenomenon as radio waves are. The colors of the rainbow in
the blue sky are there because of electricity. Cars, planes, trains can only
run because of electricity. Horses need electricity because muscle contractions
require electricity. Your nerve system is driven by electricity. Atoms,
molecule, all chemical reactions exist because of electricity.<o:p></o:p></i></div>
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<i>You could not see
without electricity. Your heart would not beat without electricity. And you could
not even think without electricity, though I realize that even with electricity
some of you may have a problem with that.</i>“ [Walter Lewin] </div>
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1.2. Modern model of
atom </h2>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_7-kS2TvJdoGd8D5jMjnQk35gIBpCY9ADs5nsbawyrXl2xh1nUZgU1aSDWgwkuEigmJZ9VtzxUvmByyxNDqYD8b5FE7VJ-j98gOX2ls90FhILPxgtQJM5eyICPhWkT_GJTsicg4wWnbxs/s1600/Figure+1.1+-+modern+atom.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="257" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_7-kS2TvJdoGd8D5jMjnQk35gIBpCY9ADs5nsbawyrXl2xh1nUZgU1aSDWgwkuEigmJZ9VtzxUvmByyxNDqYD8b5FE7VJ-j98gOX2ls90FhILPxgtQJM5eyICPhWkT_GJTsicg4wWnbxs/s400/Figure+1.1+-+modern+atom.jpg" width="400" /></a></div>
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Figure 1.1 – Modern Picture of Atom</div>
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Table 1.1 - Property of an atom</div>
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<tbody>
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<br /></div>
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Neutron</div>
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Proton</div>
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Electron</div>
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Diameter size (m)</div>
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<br /></div>
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1.2×10<sup>-15</sup></div>
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5×10<sup>-11</sup> to 5×10<sup>-10</sup></div>
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Mass (kg)</div>
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1.675×10<sup>-27</sup></div>
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1.673×10<sup>-27</sup></div>
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9.109×10<sup>-31</sup></div>
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1.3. History of
electricity</h2>
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Electron, name from a Greek word, means amber. As reported
by the ancient Greek philosopher Thales of Miletus around 600 BC, it was known
that if we rub amber that it can attract light objects such as pieces of dry
leaves and hair. So that's where electricity got its name from. </div>
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In the sev-sixteenth century there were more substances
known to do this, for instance glass and sulfur. And it was also known and
written that when people were bored at parties that the women would rub their
amber jewelry and would touch frogs. The frogs would start jumping of
desperation, which people considered to be fun, but they not understanding what
actually was happening to the amber nor what was happening to the frogs.</div>
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In 1733, C. F. du Fay proposed two varieties of electricity
that cancel each other, and expressed this in terms of a two-fluid theory. When
glass was rubbed with silk, du Fay said that the glass was charged with
vitreous electricity, and, when amber was rubbed with fur, the amber was said
to be charged with resinous electricity. Let's call one A and the other B. It
was known that A repels A and B repels B but A attracts B. </div>
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Still in the eighteenth century, it was Benjamin Franklin
without any knowledge of electrons and protons who introduced the idea that all
substances are penetrated with what he called electric fluid, electric fire.
And he stated if we get too much of the fire then we are positively charged and
if we have a deficiency of that fire, then we are negatively charged. He
introduced the sign convention and he decided that if we rub glass that that is
an excess of fire and he called that therefore positive.</div>
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We will see later that why this choice he had fifty percent chance
is extremely unfortunate but we have to live with it. So if we take this fluid
according to Benjamin Franklin and bring it from one substance to the other,
then the one that gets an excess becomes positively charged. Automatically as a
consequence of that the one - from which we take the fluid - becomes negatively
charged. </div>
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1.4. Electric charge</h2>
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Charge is an intrinsic property of partikel or matter. Charge
have been quantized and comes in multiples of individual small units called the
elementary charge, <i>e</i>, approximately
equal to 1.602×10<sup>−19</sup> Coulombs. The proton has a charge of <i>e</i>, and the electron has a charge of –<i>e</i>. </div>
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A neutral atom has same number of electron and proton, so
the charge is 0. If we take one electron off, the atom will become a positive
ion. If we add an electron then, the atom will become a negative ion. Remember,
we can't add or taking off a proton from an atom.</div>
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The electric charge is a fundamental conserved property of
some subatomic particles. This is the same as the idea of Benjamin Franklin. We
can't create charge. If we create plus then we automatically create minus.</div>
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1.4.1. Electric charging</h3>
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The question is “how can we
manipulate or engineering the electricity?”</div>
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That because we are able to
separate positive and negative charge from each other. This process called
charging and there are three methods to do that.</div>
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1.4.1.1. Friction</h4>
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From the history above, people has
been known that friction can produce positive and negative charge. Charging by
friction can happen since the two objects are made of different materials, so
their atoms bounded their electrons with different strengths. As they pass over
each other the electrons with weaker bonds are “ripped” off of that material
and collect on the other material.</div>
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1.4.1.2. Conduction</h4>
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Charging by conduction is also
called by contact. The principle is when we contact a neutral material with a
charged material, <u>the electron will be transfered</u> and neutral material
will become a charge material. But even if the material not make a contact and
just close enough to let the electron jump from one material to another
material, that is also conduction</div>
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With conduction we will get the
same type of charge. So, If we conduct with positive charged, we will get a
positive material. And if we conduct with negative charge we will get a
negative material. </div>
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1.4.1.3. Induction</h4>
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We can also charging a material
without contact or transfer of electron. This prosses called induction. As in
conduction, type of material will determine the behavior of induction. </div>
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1.4.2. Electric charge
behavior</h3>
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As we know before, same type of
charge will repel each other, and different type of charge will attract each other. But, do
you know, what it is that makes us easy to charging or not?? The answer is the
type of material. There are two type of material based on it’s electrical
property.</div>
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1.4.2.1. Conductor</h4>
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Conductor materials have moveble
electrons, so, it is easy for the electron to move from one atom to another
atom. Electrons of conductor material will move when an electric potential
difference (measured in volts) is applied across separate points on the
material. </div>
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Because of easy movement
electron, it is easy to charging the conductor material by conduction method.
The opposite, it is more complex process to charging the conductor material
with induction method.</div>
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Figure 1.2 – Conduction
and induction of conductor material</div>
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1.4.2.2. Insulator or
non-conductor</h4>
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The electrons of insulator
material are tightly bound and localized in direction of chemical bounding. So,
it is hard for the electron to move from one atom to another atom. Perferct
insulator does not respond to an electric field and completely resists the flow
of electric charge. But in real, there is no perfect insulator, so almost of
the material are semiconductor material.</div>
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In practice, the insulator can be
polarized by an applied electric field, and it called dielectric material. When
a dielectric is placed in an electric field, electric charges do not flow
through the material as they do in a conductor, but only slightly shift from
their average equilibrium positions causing dielectric polarization. Therefore,
dielectric materials with high dielectric constants (not easy to polarized)
such as glass, paper or Teflon are considered as good electrical insulators.</div>
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Dielectric property makes easy to
charging non conductor material by induction method. Rather than that, it is
more complex process to charging the insulator material with conduction method
due to only the specific areas that actually touched would show any change in charge.
</div>
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Figure 1.3 – Conduction and
induction of insulator material</div>
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1.4.2.3. Spark phenomenon</h4>
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An electric spark is a type of
electrostatic discharge that occurs when an electric field with strength
exceeds the dielectric field strength of air. This exceeded field strength
causes an increase in the number of free electrons and ions in the air and
temporarily causing the air to become an <i>ionized
electrically conductive channel</i>. This process producing a brief emission of
light and sound, and that usually we call spark. </div>
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Electric sparks occur in or near
many man-made objects. Some of them are small and some of them are large. Sometimes
it can happen by accident, and sometime it is by design. Lightning is an
example of an electric spark in nature. A continuous discharge of electric
current through a gas is an electric arc.</div>
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1.4.3. Conservation of
charge</h3>
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The total electric charge of an
isolated system remains constant regardless of changes within the system
itself. Charge cannot be created. If we create plus then automatically we
create minus. This law is inherent to all processes known to physics and can be
derived in a local form from gauge invariance of the wave function. The
conservation of charge results in the charge-current continuity equation. More
generally, the net change in charge density <i>ρ</i>
within a volume of integration <i>V</i> is
equal to the area integral over the current density <i>J</i> through the closed surface <i>S</i>
= <i>∂V</i>, which is in turn equal to the
net current <i>I</i>:</div>
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<br />
Thus, the
conservation of electric charge, as expressed by the continuity equation, gives
the result:</div>
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<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
<br />
The charge
transferred between times <i>t<sub>i</sub></i>
and <i>t<sub>f</sub></i> is obtained by
integrating both sides:</div>
<div class="MsoNormal" style="margin-left: .5in;">
<br />
<div class="separator" style="clear: both; text-align: center;">
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<br />
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
where <i>I</i> is the net outward current through a closed surface and <i>Q</i> is the electric charge contained
within the volume defined by the surface.</div>
<h3 style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 12.0pt; page-break-after: avoid; text-align: justify; text-indent: -.5in; text-justify: inter-ideograph;">
1.4.4. Electroscope - a
principle to measure charge</h3>
<div class="MsoNormal" style="margin-left: .5in;">
We will use various instruments to
measure charge in a quantitative way and one of the instruments that is very
simple, is called an electroscope. In general it is just a conducting rod (such
as aluminum, metal) with two pieces of tinsel at the end. The pieces of tinsel
usually from aluminum foil. And often there is a nice knob, so if we touch or
bring near enough to knob with a charged object, then because the rod is conductor,
this can conduct the charges.</div>
<div class="MsoNormal" style="margin-left: .5in;">
If we touch it with an object which
is positively charged, then this electroscop will become positively charged. If
I touch it with an object which is negatively charged it will become negatively
charged. If we induce the knob with positive charged, the knob will become
negative charged and the the pieces of tinsel will become positive charged. At
the end, we will see that the two very light pieces of aluminum foil will repel
each other and shows a certain angle, and the more charge there is the larger
that angle.<br />
<div class="separator" style="clear: both; text-align: center;">
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<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
<div style="text-align: center;">
Figure 1.4 – Electroscope and
example of measurement</div>
</div>
<h2 style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 27.0pt; margin-right: 0in; margin-top: 12.0pt; page-break-after: avoid; text-align: justify; text-indent: -27.35pt; text-justify: inter-ideograph;">
1.5. Electric force</h2>
<div class="MsoNormal">
It was Charles Augustin de Coulomb, French physicist, who
did a lot of research on this in the nineteenth, eighteenth century actually.
He found a special relationship between two charges. It was first published in
1785 and was essential to the development of the theory of electromagnetism.
Before it was published, other researchers have been insights into aspects of
Coulomb's law. In 1767, Joseph Priestley of England conjectured that the force
between charges varied as the inverse square of the distance.</div>
<div class="MsoNormal">
Coulomb's law or Coulomb's inverse-square law is a law of
physics describing the electrostatic interaction between electrically charged
particles. Coulomb found that the force is proportional to the product of the
two charges, times a constant, which nowadays we call Coulomb's constant, K,
and then divided by the distance between these charges squared. </div>
<div class="MsoNormal">
Now let's try a little bit more quantitative. If we take two
charges and we use for charges the symbol <i>q</i><sub>1</sub>
and <i>q</i><sub>2</sub>. They are separated
by a distance, <i>r</i>, and the unit vector
in the direction from one to two that we called <i>r</i> roof <sub>1,2</sub>. (The roof stands for unit vector). If these
charges are equal, both minus or both plus, then charges will repel each other.
The F<sub>1,2</sub> is the force on two due to number one. Since action equals
to minus reaction, force F<sub>2,1</sub> is equal to F<sub>1,2</sub> in
magnitude but a hundred eighty degrees, or it is in opposite direction.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicrtslWoseRtFrk4AdzIzKpEg6qWSKGJlzwdC2ZCN1YvU77P50Z7KiJApaJ_kwZJSI7whJYCwvnTddE9Ra6artdRejynJj_DOmeI8X-4FXFA02Lhb2KRjz1nCxAzi276bG2kyhifoeUDzG/s1600/Figure+1.5+-+Force+between+two+charges+.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicrtslWoseRtFrk4AdzIzKpEg6qWSKGJlzwdC2ZCN1YvU77P50Z7KiJApaJ_kwZJSI7whJYCwvnTddE9Ra6artdRejynJj_DOmeI8X-4FXFA02Lhb2KRjz1nCxAzi276bG2kyhifoeUDzG/s1600/Figure+1.5+-+Force+between+two+charges+.jpg" /></a></div>
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
Figure 1.5 – Electric
force between two charges</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="height: 108px; left: -1px; position: relative; top: 16px; width: 584px; z-index: 251660288;">
</span></div>
<table align="left" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td height="0" width="0"></td>
<td width="1"></td>
<td width="78"></td>
<td width="505"></td>
</tr>
<tr>
<td height="41"></td>
<td align="left" colspan="3" valign="top"><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwUhKLZ1deY5unBQHzrfW19iPsZcMmvILO1rg25M2_tHa-LWSOeXwlfFFdq3zIGm_1BHc9i2ZbTvWGvB2DyhgU5JmRNRpWHoZ5wqTNxEk1UpwInQVauhvSDSi2uW65IEceaKZIOGZ9ed-8/s1600/1-4.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwUhKLZ1deY5unBQHzrfW19iPsZcMmvILO1rg25M2_tHa-LWSOeXwlfFFdq3zIGm_1BHc9i2ZbTvWGvB2DyhgU5JmRNRpWHoZ5wqTNxEk1UpwInQVauhvSDSi2uW65IEceaKZIOGZ9ed-8/s1600/1-4.jpg" /></a></div>
</td></tr>
</tbody></table>
<div style="text-align: -webkit-left;">
<br /></div>
<div style="text-align: -webkit-left;">
Where:</div>
<div class="MsoNormal">
q= charge [Coulomb]</div>
<div class="MsoNormal">
r = distance [m]</div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2W0moLyUKX5k8Eq4YXJFdU1KwDwQpiXUXzU_tfO2Sk8OkyCozIf3NiPJk1Odegi4yR4z81jP_157jigJTBg8hVi04Sup4zr3eiMKucqjhMASU_svPWeNo6CcpcxcrgzfxXXxulkLJ_F2h/s1600/1-4b.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2W0moLyUKX5k8Eq4YXJFdU1KwDwQpiXUXzU_tfO2Sk8OkyCozIf3NiPJk1Odegi4yR4z81jP_157jigJTBg8hVi04Sup4zr3eiMKucqjhMASU_svPWeNo6CcpcxcrgzfxXXxulkLJ_F2h/s1600/1-4b.jpg" /></a></div>
K= coulomb’s contant = 8.987551787 × 10<sup>9</sup> [Nm<sup>2</sup>/Coulomb<sup>2</sup>]
= </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
<br />
<br /></div>
<h3 style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 12.0pt; page-break-after: avoid; text-align: justify; text-indent: -.5in; text-justify: inter-ideograph;">
1.5.1. Superposition</h3>
<div class="MsoNormal" style="margin-left: .5in;">
If there is three or more charge,
we can use the superposition principal. In other time we will discuss about
that.</div>
<h3 style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 12.0pt; page-break-after: avoid; text-align: justify; text-indent: -.5in; text-justify: inter-ideograph;">
1.5.2. Electricity force vs
gravitational force vs nuclear force</h3>
<div class="MsoNormal" style="margin-left: .5in;">
Look at what Joseph Priestley found
and see equation (1-1), I suddenly remember to the Newton law’s of gravitation.
</div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjDZWKZlE7QtcsD_USHTO_UsSPqgGJ6GgjLswk8PTZemrHiJI-bsgoxoWyHDkSjPr7gu3W3w7EjjiXvkBNo4JfSCs-aJZVRGao7adAjAKE6LhVreN0jN-o4eeWUNo_IyX5-gCydEZ0FlGB/s1600/Figure+1.6+-+Gravity+force+between+two+masses+.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjDZWKZlE7QtcsD_USHTO_UsSPqgGJ6GgjLswk8PTZemrHiJI-bsgoxoWyHDkSjPr7gu3W3w7EjjiXvkBNo4JfSCs-aJZVRGao7adAjAKE6LhVreN0jN-o4eeWUNo_IyX5-gCydEZ0FlGB/s1600/Figure+1.6+-+Gravity+force+between+two+masses+.jpg" /></a></div>
<br /></div>
<div align="center" class="MsoNormal" style="margin-left: .5in; text-align: center;">
Figure 1.6 – Gravitational force
between two mass</div>
<table align="left" cellpadding="0" cellspacing="0"><tbody>
<tr><td></td>
<td height="36" style="vertical-align: top;" width="59"><br /></td></tr>
</tbody></table>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZvUSR9Su6Qr8DTs3SKD-IyplhpmEuEFFobxPAFIqmdoBCTDvAW8dLlF40jm17bMDpkhvXTs5nMNJ6MObIuEtUgNhaLnJ_GBT2YHp29PqAVcZ04rodf21XWUFiSvNXQVfNSTyrw0itNw9u/s1600/1-5.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZvUSR9Su6Qr8DTs3SKD-IyplhpmEuEFFobxPAFIqmdoBCTDvAW8dLlF40jm17bMDpkhvXTs5nMNJ6MObIuEtUgNhaLnJ_GBT2YHp29PqAVcZ04rodf21XWUFiSvNXQVfNSTyrw0itNw9u/s1600/1-5.jpg" /></a><br />
<div class="MsoNormal" style="margin-left: .5in;">
<br />
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
Where:
<br />
m = mass [kg]
<br />
r
= distance [m] </div>
<div class="MsoNormal" style="margin-left: .5in;">
G = gravitational contant [Nm<sup>2</sup>/kg<sup>2</sup>]
= 6.674 × 10<sup>-11</sup> [Nm<sup>2</sup>/coulomb<sup>2</sup>]</div>
<div class="MsoNormal" style="margin-left: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
And if we compare electricity &
magnetism with mechanical, thereby comparing electricity with gravity, we will
see that electric forces are way more powerful than gravitational force. Let’s
see that is by taking two protons which are a distance D apart. As they have
the same charged, they will repel each other, because of electric force. Remember
of Table 1.1, we know that the proton have mass. Because gravity always attract
each other, so it will become force that opposite to the electric. Now, the
question is “which one is more powerfull?”</div>
<div class="MsoNormal" style="margin-left: .5in;">
<br /></div>
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<div class="separator" style="clear: both; text-align: center;">
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<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
<div style="text-align: center;">
Figure 1.7 – Example of force
acting on protons</div>
</div>
<div class="MsoNormal" style="margin-left: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
<br />
To answer the question, let’s use
equation (1-4) and equation (1-5) with the data from Tabel 1.1:<br />
<div class="separator" style="clear: both; text-align: center;">
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<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
From the result above, we found
that the electric force is thirty-six orders of magnitude more potent than the
gravitational attraction. If these were the only forces that acted on the
protons and you bring them in the nucleus, which has a size of only ten to the
minus fourteen meters, then the acceleration that the proton will experience is
the electric force divided by the mass of the proton. If there is two protons
in an atom, then the electric force that repel the protons each other have
ratio about twenty-six order of magnitude higher than the gravitational
acceleration on earth.</div>
<div class="MsoNormal" style="margin-left: .5in;">
As we know the gravitational
attraction is thirty-six order of magnitude lower than repelled of electric
force, ‘what kind of force that holds nucleus together?’ There must be such a
tremendous force on these protons. Well, the answer is the nuclear forces that
holding them together. We will not discuss about nuclear force on this topic,
so, just leave it alone for now.</div>
<div class="MsoNormal" style="margin-left: .5in;">
So what holds our world together?
Well …. :</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .75in; margin-right: 0in; margin-top: 0in; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -.25in; text-justify: inter-ideograph;">
i)<span style="font-size: 7pt; line-height: normal;">
</span>On the nucleus scale (about 10<sup>-14</sup>m), nuclear
force are very important.</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .75in; margin-right: 0in; margin-top: 0in; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -.25in; text-justify: inter-ideograph;">
ii)<span style="font-size: 7pt; line-height: normal;">
</span>On an atomic scale up to thousands of
kilometers, it's electric forces that hold our world together. </div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .75in; margin-right: 0in; margin-top: 0in; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -.25in; text-justify: inter-ideograph;">
iii)<span style="font-size: 7pt; line-height: normal;">
</span>But on a much larger scale, planets and stars
and the galaxy, it is gravity that dictate the behavior of the universe.</div>
<div class="MsoNormal" style="margin-left: .5in;">
After we know about that, we may
say, “That's very inconsistent with what we have learned in Figure 1.7!” Yes,
however, most objects are neutral or very close to neutral and so if you take
the earth it is very unlikely even that the earth as a whole would have a charge
of more than ten coulombs (that probably is already an exaggeration). So, if we
put the earth with ten coulombs and then we put minus ten coulombs, so they
will attract each other, but given their distance, it's almost nothing. The electric
force on that scale is negligibly small. But of course, at that scale, the
force of gravity wins, because of their massive masses. </div>
<div class="MsoNormal" style="margin-left: .5in;">
In this particular case, which we
take the earth and the moon, the gravitational force wins over the electric
force by twenty-five orders of magnitude. So even though our immediate
surroundings are dominated by electric forces, including our own body for that
matter, the behavior of the universe on a large scale is dictated by gravity.</div>
<div class="MsoNormal" style="margin-left: .5in;">
<br />
<br />
<br />
<br /></div>
<div class="MsoNormal" style="margin-left: 27.0pt; text-indent: -27.0pt;">
<br /></div>
<h1 style="margin-left: 13.5pt;">
Bibliography</h1>
<div class="MsoBibliography">
<br /></div>
<div class="MsoBibliography">
<br />
<div class="MsoBibliography">
<i>Charging</i>. (n.d.). Retrieved April 17, 2012, from
www.studyphysics.ca: <a href="http://www.studyphysics.ca/30/charging.pdf">http://www.studyphysics.ca/30/charging.pdf</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Conductors
Insulators and Induced Charged</i>.
(n.d.). Retrieved April 17, 2012, from physics.unl.edu: <a href="http://physics.unl.edu/~cbinek/Unit_2%20conductors%20insulators%20and%20induced%20charges.pptx">http://physics.unl.edu/~cbinek/Unit_2%20conductors%20insulators%20and%20induced%20charges.pptx</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Coulomb's law</i>. (n.d.). Retrieved April 19, 2012, from en.wikipedia.org:
<a href="http://en.wikipedia.org/wiki/Coulomb%27s_law">http://en.wikipedia.org/wiki/Coulomb%27s_law</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Dielectric</i>. (n.d.). Retrieved April 19, 2012, from
en.wikipedia.org: <a href="http://en.wikipedia.org/wiki/Dielectric">http://en.wikipedia.org/wiki/Dielectric</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Electric charge</i>. (n.d.). Retrieved April 16, 2012, from
en.wikipedia.org: <a href="http://en.wikipedia.org/wiki/Electric_charge">http://en.wikipedia.org/wiki/Electric_charge</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Electric Spark</i>. (n.d.). Retrieved April 17, 2012, from
en.wikipedia.org: <a href="http://en.wikipedia.org/wiki/Electric_spark">http://en.wikipedia.org/wiki/Electric_spark</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Electrical conductor</i>. (n.d.). Retrieved April 17, 2012, from
en.wikipedia.org: <a href="http://en.wikipedia.org/wiki/Electrical_conductor">http://en.wikipedia.org/wiki/Electrical_conductor</a>
<o:p></o:p></div>
<div class="MsoBibliography">
Ganderton. (n.d.). <i>What
is the charge and location and mass of a proton and a neutron and an electron
in the atom?</i> (JEK, Editor) Retrieved April 15, 2012, from wiki.answers.com:
<a href="http://wiki.answers.com/Q/What_is_the_charge_and_location_and_mass_of_a_proton_and_a_neutron_and_an_electron_in_the_atom">http://wiki.answers.com/Q/What_is_the_charge_and_location_and_mass_of_a_proton_and_a_neutron_and_an_electron_in_the_atom</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Insulator
(electricity)</i>. (n.d.). Retrieved
April 17, 2012, from en.wikipedia.org: <a href="http://en.wikipedia.org/wiki/Electrical_insulation">http://en.wikipedia.org/wiki/Electrical_insulation</a>
<o:p></o:p></div>
<div class="MsoBibliography">
<i>Newton's law of
universal gravitation</i>. (n.d.).
Retrieved April 19, 2012, from en.wikipedia.org: <a href="http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation">http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation</a>
</div>
<div class="MsoBibliography">
Lewin, Walter, <i>8.02
Electricity and Magnetism, Spring 2002 </i>(Massachusetts Institute of
Technology: MIT OpenCourseWare). <u><a href="http://ocw.mit.edu/">http://ocw.mit.edu</a></u>
(accessed April 19, 2012). License: Creative Commons
Attribution-Noncommercial-Share Alike.<span style="font-family: "NVOLCK+Verdana","sans-serif"; mso-bidi-font-family: NVOLCK+Verdana;"><o:p></o:p></span></div>
</div>
<div class="MsoBibliography">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><br /></span>
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><br /></span>
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><br /></span>
<br />
<div style="text-align: center;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">********THANK to GOD*******</span></div>
</div>
skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-18103579433295741362012-03-23T14:12:00.009-07:002014-09-27T11:07:37.426-07:00FLIGHT MECHANICS1.1. Understanding<br />
Flight mechanics is a study about the forces act on the aircraft or spacecraft, that cause the motion. This study is application of Newton’s Law to the aircraft or spacecraft. The motion of aircraft have two kind of references. First is a point outside the aircraft or spacecraft, and second is center of gravity on the aircraft or spacecraft. This references are basic for the classification in the branch of flight mechanics.<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzh0RWNWf4I0QhXBd-kEFW9M-SxCIthzV448He_L87ac1Bor10-Uo0ro3ceXjj88HRc0jxXf-wNw2u7fyvxmXqo6d7-V0NAgfiVyLNwfKpSN988_s1s9mGMy3Fr91AFnsWsPo1HySXC7eV/s1600/Figure+1+-+a.+Outer+point+reference.jpg"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzh0RWNWf4I0QhXBd-kEFW9M-SxCIthzV448He_L87ac1Bor10-Uo0ro3ceXjj88HRc0jxXf-wNw2u7fyvxmXqo6d7-V0NAgfiVyLNwfKpSN988_s1s9mGMy3Fr91AFnsWsPo1HySXC7eV/s400/Figure+1+-+a.+Outer+point+reference.jpg" id="BLOGGER_PHOTO_ID_5723203653134230226" style="cursor: hand; cursor: pointer; display: block; height: 287px; margin: 0px auto 10px; text-align: center; width: 400px;" /></a><br />
<div style="text-align: center;">
(a) Outer reference point</div>
<br />
<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgngaQTTCVFQIeU7Y3KhrR6x5pXx0UEn-AeLRmy2zirU4DPe05wewV0L-RakNVCqW48lzhe1UhtTX0X1pBCjqnt303tu-TCVf3qTFVW0vP62cmFKE8gAGKEwEB8LPJ62Ic5UyVe-t0m7MhQ/s1600/Figure+1+-+b.+Reference+point+at+CG+.jpg"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgngaQTTCVFQIeU7Y3KhrR6x5pXx0UEn-AeLRmy2zirU4DPe05wewV0L-RakNVCqW48lzhe1UhtTX0X1pBCjqnt303tu-TCVf3qTFVW0vP62cmFKE8gAGKEwEB8LPJ62Ic5UyVe-t0m7MhQ/s400/Figure+1+-+b.+Reference+point+at+CG+.jpg" id="BLOGGER_PHOTO_ID_5723204059159061810" style="cursor: hand; cursor: pointer; display: block; height: 276px; margin: 0px auto 10px; text-align: center; width: 378px;" /></a><br />
<div style="text-align: center;">
(b) Reference point attach to the center of gravity</div>
<br />
<br />
<div style="text-align: center;">
Figure 1. Different kind of Motion Reference</div>
<br />
<br />
1.2. Classification<br />
As we know before, different reference points of motion will result in different treatment to analize. This causing flight machanics have four main brances of study.<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgna5vhK03ybEmDTOw4gbLmuLfR998l2vMbCWWCmNXcjGWaJC44KDtWS36JWUeQmaXnNy152WyqDUn5hX21lTpl75mEfX8JYolSoT2WBx15lz_93tC-pPOZnMotQZHIHj1dXyGjBoaTdIxs/s1600/Figure+2+-+The+Branch+of+Flight+Mechanics+.jpg"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgna5vhK03ybEmDTOw4gbLmuLfR998l2vMbCWWCmNXcjGWaJC44KDtWS36JWUeQmaXnNy152WyqDUn5hX21lTpl75mEfX8JYolSoT2WBx15lz_93tC-pPOZnMotQZHIHj1dXyGjBoaTdIxs/s400/Figure+2+-+The+Branch+of+Flight+Mechanics+.jpg" id="BLOGGER_PHOTO_ID_5723204462104823858" style="cursor: hand; cursor: pointer; display: block; height: 219px; margin: 0px auto 10px; text-align: center; width: 400px;" /></a><br />
<div style="text-align: center;">
Figure 2. Study brunches of Flight Mechanics</div>
<br />
a. Flight performance (dreaming time)<br />
Flight performance is a branch of flight mechanics that study about flight vehicle performance along the path, due to all force acting on it. The vehicle is representated by its center of gravity<br />
Input: major or dominant force<br />
Output: distance, endurance, speed, etc<br />
Common issue: speed, economics flight, distance, fuel, etc<br />
<br />
<br />
<br />
b. Flight Guidance / Navigation (start point)<br />
Flight Guidance is a study about how to guidance the flight vehicle through its cours or path that has been planned.<br />
Input: Flight plan, course, destination,<br />
Output: Flight path<br />
Common issue: optimal course/path, Minimal fuel for space travel, etc.<br />
<br />
c. Flight Dynamics<br />
Flight Dynamics is a study that learn about the attitude of flight vehicle and the respon to the inner force or disturbance acting on it.<br />
Input: inner force, disturbance, dumping character, vehicle configuration, etc.<br />
Output: vehicle stability character<br />
Common issue: stability of the aircraft when there are disturbance acting on it.<br />
<br />
<br />
d. Flight Control and Stability<br />
Flight Control is a branch of flight mechanics that study about how to reach or to keep the attitude of the flight vehicle.<br />
Input: aerodynamic force, thrust, etc<br />
Output: optimal respons, stability, etc<br />
Common issue: how to stabilize the vehicle, maneuverability, control system loop, <br />
<br />
<br />
<br />
1.3. For a better understanding<br />
For a better understanding, I suggest you to learning or familiar with some of the list below:<br />
- Coordinat <br />
- Fligth configuration<br />
- Flight attitude<br />
- Shape parameter of flight vehicle<br />
- Some aerodynamics and astrodynamics important terms<br />
<br />
<br />
<br />
REFERENCE<br />
<br />
<br />
Jenie, S. D. (1985). DINAMIKA TERBANG (a lecture note MS 455). Bandung.skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-20618119967745581742012-03-21T13:44:00.005-07:002012-04-25T08:35:26.892-07:00AIRPLANE DESIGN<br />
<h2>
<a href="http://www.blogger.com/blogger.g?blogID=9034572127535224290" name="_Toc250721772"><span style="font-size: large;">1.1.<span style="font-weight: normal;">
</span>Design your own aircraft, why not?!</span></a></h2>
<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 0in;">
It is hi-tech, complicated, and I feel so
challenge.</div>
<h2>
<span style="font-size: large;">
1.2.<span style="font-weight: normal;"> </span>Design
process</span></h2>
<div class="MsoNormal">
From many
reference, and experience of design other thing, I conclude, there are three
main process in design airplane:</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo1; text-indent: -.25in;">
a.<span style="font-size: 7pt;">
</span>Conceptual design</div>
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</div>
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<br /></div>
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</div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieFOJZhhqrrR-FxXbEVMH5mRthmHiUjp92g69rdG8JEvAagiZahRteqkvpJM9HUIWPNnWnQY4VIoD1uTSwLKxhjphLeNpdzfx3F0KBHBSLCgsBZX8LmWEFBfFyzQ7JcdhR_QIJORFEHJ4g/s1600/Figure+1+-+Conseptual+Design+Process+.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieFOJZhhqrrR-FxXbEVMH5mRthmHiUjp92g69rdG8JEvAagiZahRteqkvpJM9HUIWPNnWnQY4VIoD1uTSwLKxhjphLeNpdzfx3F0KBHBSLCgsBZX8LmWEFBfFyzQ7JcdhR_QIJORFEHJ4g/s1600/Figure+1+-+Conseptual+Design+Process+.jpg" /></a></div>
Figure 1. Conseptual
Design Process</div>
<div class="MsoNormal" style="margin-left: .25in; text-indent: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .25in; text-indent: 0in;">
This process consist of:</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>Collecting data</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>Make a Matching Chart</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>Compromising the configuration</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l2 level1 lfo3; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>Determine initial/preliminary sizing</div>
<div class="MsoNormal" style="margin-left: .25in; text-indent: 0in;">
<br /></div>
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<br /></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo1; text-indent: -.25in;">
b.<span style="font-size: 7pt;">
</span>Initial / preliminary design (start point)</div>
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<br /></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7UyDQg5jfUPWBO0meW84J_L8oM-DUyqSR3O7KRYMqyJmiEoOtrN7E0Q5jnx82Bo_qDK8b41Zbszs3kCg9NRKyLC6C66csK1JUrJB3UgoE1_ZM5sGyfU1tMyadD_94cha27n8nO8z-_JnD/s1600/Figure+2+-+Preliminary+Design+Process+.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7UyDQg5jfUPWBO0meW84J_L8oM-DUyqSR3O7KRYMqyJmiEoOtrN7E0Q5jnx82Bo_qDK8b41Zbszs3kCg9NRKyLC6C66csK1JUrJB3UgoE1_ZM5sGyfU1tMyadD_94cha27n8nO8z-_JnD/s1600/Figure+2+-+Preliminary+Design+Process+.jpg" /></a></div>
<div align="center" class="MsoNormal" style="margin-left: .25in; text-align: center; text-indent: 0in;">
Figure 2. Preliminary
Design Process</div>
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<br /></div>
<div class="MsoNormal" style="margin-left: .25in; text-indent: 0in;">
Preliminary design process can be classification in two major
process.</div>
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1)<span style="font-size: 7pt;">
</span>Initial:</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l0 level2 lfo5; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Initial
layout of wing and fuselage</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l0 level2 lfo5; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Analizing
class I: Tail Sizing, Weight and Balance, Drag Polar</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l0 level2 lfo5; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Initial
Landing Gear Disposition</div>
<div class="MsoNormal" style="margin-left: .5in; text-indent: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l1 level1 lfo4; text-indent: -.25in;">
2)<span style="font-size: 7pt;">
</span>Reviced</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l3 level2 lfo6; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Layout
of Wing, Fuselage and Empennage</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l3 level2 lfo6; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Analizing
class II: Tail Sizing, Weight and Balance, Drag Polar, Flaps Effects, Stability
and Control.</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l3 level2 lfo6; tab-stops: 187.5pt; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span>Performance Verification </div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l3 level2 lfo6; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Preliminary
Structural Layout</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l3 level2 lfo6; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Landing
gear Disposition and retraction check</div>
<div class="MsoNormal" style="margin-left: .75in; mso-list: l3 level2 lfo6; text-indent: -.25in;">
<span style="font-family: 'Courier New';">o<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Cost
Calculation</div>
<div class="MsoNormal" style="margin-left: .5in; text-indent: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo1; text-indent: -.25in;">
c.<span style="font-size: 7pt;">
</span>Detail design</div>
<div align="center" class="MsoNormal" style="margin-left: .25in; text-align: center; text-indent: 0in;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
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Figure 3. Detail
Design Process</div>
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<br /></div>
<div class="MsoNormal" style="margin-left: .25in; text-indent: 0in;">
<br /></div>
<div class="MsoNormal">
To get the best
solution the process is never stop on those three process. The other process is
analazing design. We can analize the design with data that we get from from
these two process:</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo1; text-indent: -.25in;">
d.<span style="font-size: 7pt;">
</span>Manufacturing / producing</div>
<div class="MsoNormal" style="margin-left: .25in; mso-list: l4 level5 lfo1; text-indent: -.25in;">
e.<span style="font-size: 7pt;">
</span>Maintanance</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
If something wrong
or to far from what you expect, the result/report will be come feedback for
earlier process. Example, after you producing, the airplane fuel consumption is
too high, so you have to go back to detail, preliminary or even the conceptual
design to make the fuel consumption is more acceptable.</div>
<h2>
<span style="font-size: large;">
1.3.<span style="font-weight: normal;">
</span>Design Tools</span></h2>
<div class="MsoNormal" style="margin-left: 45.0pt; mso-list: l5 level1 lfo2; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>Modeling tool: tools to create mathematical model of
physical properties. Example: Microsoft Exel, MathLab, DATCOM, AAA, FLUENT,
X-Foil, etc.</div>
<div class="MsoNormal" style="margin-left: 45.0pt; mso-list: l5 level1 lfo2; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>Drawing tool. Example: CATIA, AUTOCAD, etc.</div>
<div class="MsoNormal" style="margin-left: 45.0pt; mso-list: l5 level1 lfo2; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>Report</div>
<div class="MsoNormal" style="margin-left: 45.0pt; mso-list: l5 level1 lfo2; text-indent: -.25in;">
-<span style="font-size: 7pt;">
</span>The last but the most important: GOD Blessing <span style="font-family: Wingdings;">J</span></div>
<h1 style="margin-left: 0in; mso-list: none;">
<br /></h1>
<h1 style="margin-left: 0in; mso-list: none;">
<span style="font-size: large;">
BIBLIOGRAPHY</span><o:p></o:p></h1>
<div class="MsoBibliography">
Raymer, D. P. (1992). <i>Aircraft
Design: A Conceptual Approach.</i> Washington, DC: American Institute of
Aeronautics and Astronautics, Inc.<o:p></o:p></div>
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 150%;">Roskam, I. (1885). <i>PART I:
PRELIMINARY SIZING OF AIRPLANES.</i> Lawrence, Kansas: Roskam Aviation and
Engineering Corporation.</span>skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-85972737128398781092011-12-18T12:22:00.000-08:002012-08-20T14:50:58.199-07:00ACTUATOR pada ROBOTHiiii semua-nya, pada bagian ini kita akan membahas mengenai actuator yang umumnya digunakan dalam dunia robotika, khususnya yang berbasis elektronik. Ada 3 jenis actuator/transduser dasar penghasil gerak yang umum digunakan, yaitu:<br />
1. Motor DC standar<br />
2. Motor Servo<br />
3. Motor stepper<br />
Ketiga jenis transduser diatas ini akan mengubah energi listrik/elektromagnetik menjadi energi gerak mekanik berupa gerakan rotasi atau torsi. Dengan menggunakan mekanika transformator lainnya, gerakan rotasi tersebut dapat dibuah menjadi gerakan translasi atau gerakan lain yang diinginkan. Penjelasan lebih lanjut mengenai ketiga jenis penggerak tersebut dapat diliat pada sub bagian dibawah ini:<br />
A. Motor DC standar<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfMGk5rB4TTXXQWJ6Ifrfx6L3R0JUkU0AGt0Urb2txiY8Ii0kcjXQ_U42_IUWQU7HAKgeEmr2655Vln7sg_BxnROIi_j71S_tGg6FVrOdxxvUnsLcj5NCgLnNLIFB_kGZZt8m2OxLRr5d9/s1600/gambar+1a+%2528www.wikimedia.org%2529+.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5687567708567656834" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfMGk5rB4TTXXQWJ6Ifrfx6L3R0JUkU0AGt0Urb2txiY8Ii0kcjXQ_U42_IUWQU7HAKgeEmr2655Vln7sg_BxnROIi_j71S_tGg6FVrOdxxvUnsLcj5NCgLnNLIFB_kGZZt8m2OxLRr5d9/s320/gambar+1a+%2528www.wikimedia.org%2529+.jpg" style="cursor: hand; cursor: pointer; display: block; height: 239px; margin: 0px auto 10px; text-align: center; width: 220px;" /></a><br />
Gambar 1 – Contoh-contoh Motor DC standar<br />
(source: <a href="http://www.wikimedia.org/">www.wikimedia.org</a> and <a href="http://www.inexglobal.com/">www.inexglobal.com</a>)<br />
Motor DC merupakan suatu rangkaian motor yang dapat merubah suatu besaran listrik menjadi suatu bentuk sistem gerak mekanik. Dari namanya saja terlihat bahwa, motor DC memerlukan sumber listrik secara searah (DC) agar dapat mengkonversinya dalam bentuk gerak mekanik. Prinsip kerja motor DC seperti yang ditunjukan pada Gambar 2.<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-u_mrEz_x0kk1APohpc8ji8i4ybr02AQ22XL-OuC8bjKqnwtB1ICtpYwA-d9wN-Qv3xoSqEcw978ngqTTEARv4vLuqhDGjF-3eR44OzJ6NPbaKs8SbW4wt2Y5Kmkq6cDvUuJa7mhnxixh/s1600/Gambar+2+-+%2528hyperphysics.phy-astr.gsu.edu%2529+.gif"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5687569438658861234" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-u_mrEz_x0kk1APohpc8ji8i4ybr02AQ22XL-OuC8bjKqnwtB1ICtpYwA-d9wN-Qv3xoSqEcw978ngqTTEARv4vLuqhDGjF-3eR44OzJ6NPbaKs8SbW4wt2Y5Kmkq6cDvUuJa7mhnxixh/s320/Gambar+2+-+%2528hyperphysics.phy-astr.gsu.edu%2529+.gif" style="cursor: hand; cursor: pointer; display: block; height: 249px; margin: 0px auto 10px; text-align: center; width: 320px;" /></a><br />
Gambar 2 – Prinsip dasar motor DC<br />
(Source: <a href="http://www.hyperphysics.phy-astr.gsu.edu/">www.hyperphysics.phy-astr.gsu.edu</a>)<br />
Keuntungan Motor DC<br />
+ Sederhana<br />
+ Paling banyak digunakan untuk mobile robot. <br />
+ Tingkat kebisingannya rendah <br />
+ Dapat memberikan daya yang memadai untuk tugas-tugas berat<br />
Kekurangan Motor DC<br />
- Belum memiliki sistem feedback (umpan balik)<br />
- Memerlukan arus yang cukup, biasanya memerlukan penguat arus (lihat gambar 3)<br />
- Memerlukan rangkaian tambahan untuk mengatur kecepatan atau posisi motor<br />
- Memerlukan rangkaian tambahan untuk mengatur arah putaran motor<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiimpCYb3dXB3m3iT1u7maF8rDzz1s8me9KJw0055FH4YTSBpgccTmnwl2Q04MbUB7rgF3jax05sQ2hJp7BI9T5o1YqxFLcvM-T0VsfpE76o4hpTbAKUDVUSMuNmtf00_AxoSXhe28azsi/s1600/gambar+3+-+penguat+arus+pada+motor+DC+.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5687570285671684146" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiimpCYb3dXB3m3iT1u7maF8rDzz1s8me9KJw0055FH4YTSBpgccTmnwl2Q04MbUB7rgF3jax05sQ2hJp7BI9T5o1YqxFLcvM-T0VsfpE76o4hpTbAKUDVUSMuNmtf00_AxoSXhe28azsi/s320/gambar+3+-+penguat+arus+pada+motor+DC+.jpg" style="cursor: hand; cursor: pointer; display: block; height: 264px; margin: 0px auto 10px; text-align: center; width: 308px;" /></a><br />
Gambar 3. Rangkaian penguat arus pada motor DC<br />
Namanya manusia, melihat kekuarangan-kekuaranga motor DC, seperti yang disebutkan diatas, pasti akan merasa tidak puas. Oleh karena itu orang berusaha untuk mengembangkan 2 jenis actuator baru. Karena merupakan pengembangan, kedua jenis actuator ini, yaitu motor servo dan motor stepper, masih menggunakan motor DC sebagai komponen utamannya. Penjelasan lebih lanjut mengenai motor servo dan motor stepper dapat dilihat pada sub bagian selanjutnya.<br />
B. Servo Motor<br />
Sebagai pengembangan dari motor DC, motor Servo memiliki beberapa tambahan beberapa komponen elektronika dan gear makanik. Tambahan komponen elektronik digunakan agar servo dapat dikendalikan dengan metoda PWM. Sedangakan gear-gear mekanik berfungsi untuk meningkatkan keakuratan dari perputaran motor DC di dalamnya, sehingga pengguna motor servo dapat mengendalikan posisi rotasi motor servo. <br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTKs-AAj-Kz25iksUWug_FG5xDQMgH-UkUESLw6rxfY6DCvA3LCe3E_uZOAhyOU4jS9Uc78BgYd0LRJd7IIg5Ej4rlJMS_gbtmYaZ_0oW6o7eKp9PoUj54ks-P-EVZZVp6VJgYcZ3Tyg2L/s1600/Gambar+4b+-+%2528www.seattlerobotics.org%2529.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5687570675158403138" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTKs-AAj-Kz25iksUWug_FG5xDQMgH-UkUESLw6rxfY6DCvA3LCe3E_uZOAhyOU4jS9Uc78BgYd0LRJd7IIg5Ej4rlJMS_gbtmYaZ_0oW6o7eKp9PoUj54ks-P-EVZZVp6VJgYcZ3Tyg2L/s320/Gambar+4b+-+%2528www.seattlerobotics.org%2529.jpg" style="cursor: hand; cursor: pointer; display: block; height: 240px; margin: 0px auto 10px; text-align: center; width: 320px;" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsoEektBSlZwDukl_lb3KWA3bVUMbpwTISnsoKcFf8OuI5NBUyFIeZAcGiyJ9Qu7Qhy_SXNaymrkZk4omSvQEwE9YM4ojplj_AWv599P69u0M7XU4E8NCMAFYTWAt7KJvyj9XdLWXN8ArT/s1600/gambar+4+-+%2528www.pyroelectro.com%2529.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5687570672154582258" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsoEektBSlZwDukl_lb3KWA3bVUMbpwTISnsoKcFf8OuI5NBUyFIeZAcGiyJ9Qu7Qhy_SXNaymrkZk4omSvQEwE9YM4ojplj_AWv599P69u0M7XU4E8NCMAFYTWAt7KJvyj9XdLWXN8ArT/s320/gambar+4+-+%2528www.pyroelectro.com%2529.jpg" style="cursor: hand; cursor: pointer; display: block; height: 281px; margin: 0px auto 10px; text-align: center; width: 300px;" /></a><br />
Gambar 4. Motor Servo<br />
(Source: <a href="http://www.pyroelectro.com/">www.pyroelectro.com</a> and <a href="http://www.seattlerobotics.org/">www.seattlerobotics.org</a>)<br />
Motor servo sendiri mempunyai 3 kabel, yaitu Vcc, ground dan PWM input (lihat Gambar 5). Tidak seperti PWM pada motor stepper, input sinyal untuk servo tidak digunakan untuk mengatur kecepatan, tetapi digunakan untuk mengatur posisi dari putaran servo. Sinyal PWM untuk servo mempunyai yang frekuensi 50 Hz, maka pulsa yang dihasilkan memiliki periode 20ms. Sebagai contoh, sebuah pulsa 0.7ms akan memutarkan disk servo ke posisi kiri (-120 derajat), dan pulsa 1.7ms akan memutarkan disk ke posisi kanan (+120 derajat). Ada dua jenis servo yang umumnya digunakan:<br />
a. Servo motor standar dilengkapi dengan motor DC untuk mengendalikan posisi sebuah robot. Rotor motor dapat diputar/diposisikan hingga 180 derajat. <br />
b. Servo motor continuous, dapat berputar hingga 360 derajat. Umumnya kita membeli servo continuous karena dapat berputar 360 derajat, namun anehnya harganya lebih murah dibandingkan servo standar yang derajat putarannya terbatas.<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB-BczFZsHrnQcqvA1UYZwX5SFM3L_eGlhBvJDWqN2Zv-7guq5Z6itdvpq_ffp3wBtPNcSn16H40p1UkeSxA21l-D5O4jM6DJADPQf38lL9PdaJUvuu1n4vvhHAWu5ZroNYAND0Pnizl2c/s1600/gambar+5+-+%2528alan-parekh.com%2529+.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5687570898562999042" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB-BczFZsHrnQcqvA1UYZwX5SFM3L_eGlhBvJDWqN2Zv-7guq5Z6itdvpq_ffp3wBtPNcSn16H40p1UkeSxA21l-D5O4jM6DJADPQf38lL9PdaJUvuu1n4vvhHAWu5ZroNYAND0Pnizl2c/s320/gambar+5+-+%2528alan-parekh.com%2529+.jpg" style="cursor: hand; cursor: pointer; display: block; height: 225px; margin: 0px auto 10px; text-align: center; width: 320px;" /></a><br />
Gambar 5. Input-output pada motor servo.<br />
Servo motor biasa digunakan untuk mengendalikan gerak dari toys (mainan) , hobist, pada pesawat terbang model, mobil, kapal, pesawat, perahu, atau helikopter. Aplikasi servo umumnya pada sistem closed control loop. Motor tersebut harus dapat menangani perubahan yang cepat pada posisi, kecepatan dan percepatan, serta harus mampu menangani intermittent torque.<br />
Kelebihan Servo motor:<br />
Memiliki daya output yang relatif tinggi dibanding dimensi dan beratnya.<br />
Encoder determines accuracy and resolution.<br />
Tingkat efisiensi tinggi, dapat mencapai 90% untuk beban yang ringan<br />
Rasio perbandingan torsi dan inersia motor servo cukup tinggi. Hal ini menyebabkan motor servo dapat mempercepat gerakan bebannya.<br />
Memiliki tenaga “cadangan”, 2 sampai 3 kali untuk 1 periode singkat.<br />
Memiliki torsi “cadangan”, 5-10 kali untuk 1 periode yang singkat.<br />
Motor pada motor servo umumnya lebih dingin, karena servo motor umumnya digunakan pada beban yang ringan.<br />
Dapat bekerja pada torsi yang tinggi, dapat mencapai 90% dari NL RPM. <br />
Tingkat kebisingan relaitf rendah pada kecepatan tinggi. <br />
Resonance and vibration free operation.<br />
Kekurangan servo:<br />
- Tidak menyediakan feedback. <br />
- Requires "tunning" to stabilize feedback loop. Motor "runs away" when something breaks. <br />
- Memerlukan rangkaian yang aman.<br />
- Kompleks, memerlukan encoder. <br />
- Brush pada motor servo memiliki umur rata-rata hingga 2000 jam, lebih dari itu maka perlu mengalami perawatan (service).<br />
- Torsi maksimal dibatasi 1% duty cycle.<br />
- Motor dapat rusak jika mengalami kelebihan beban terus-menerus..<br />
- Bewildering choice of motors, encoders, and servo drives.<br />
- Untuk mencapai torsi maksimal membutuhkan suplai arus 10 kali kebutuhan arus rata-rata. <br />
- Motor develops peak power at higher speeds. Gearing often required.<br />
- Memiliki sistem pendinginan yang buruk, karena motor dengan ventilasi dapat mudah terkontaminasi dengan debu atau benda-benda lain yang mengganggu.<br />
<br />
C. Motor Stepper<br />
Motor stepper juga merupakan pengembangan dari motor DC biasa. Umumnya motor stepper digunakan untuk daya gerak, pengarah dan pengendali posisi robot. Motor stepper sangat unik, karena dapat dikendalikan dengan sirkuit digital, dan sangat ideal untuk menggerakkan robot secara rotasi (berputar) dan posisi linear/garis lurus. Karena digunakan pada industri secara luas, motor stepper memiliki banyak variasi, baik ukuran maupun spesifikasinya. Sangat sulit untuk memposisikan rotor dari motor stepper secara tepat. Perlu diketahui, tidak semua motor stepper memutar rotor dengan nilai yang sama tiap langkahnya, karena motor stepper dibuat dengan derajat rotasi yang berbeda-beda setiap langkahnya. Untuk menghasilkan derajat rotasi yang optimal sangat tergantung dari penggunaan motor stepper itu sendiri. Contoh derajat rotasi yang mungkin terbentuk antara lain 72 derajat dan 22.5 derajat. Putaran motor stepper juga tergantung dari nilai digital yang diberikan ke stepper tersebut.<br />
Keuntungan Motor Stepper:<br />
Stabil, karena dapat menggerakan beban dalam rentang yang luas, baik beban inersia maupun beban friksi.<br />
Tidak memerlukan umpan balik, karena motor itu sendiri juga berfungsi sebagai position transducer. <br />
Relative tidak mahal untuk berbagai sistem pengendali gerak. <br />
Standardized frame size and performance. <br />
Plug and play, artinya mudah dipasang dan digunakan. Easy to setup and use. <br />
Aman, karena saat ada yang rusak maka motor akan langsung berhenti. <br />
Memiliki umur pakai yang cukup lama. Biasanya bearing yang mengalami yang aus (wear-out).<br />
Sangat baik bekerja pada torsi yang rendah, karena dapat mengangkut beban yang banyak tanpa menggunakan sistem transmisi (gearing). <br />
Excellent repeatability. Returns to the same location accurately.<br />
Overload safe. Motor cannot be damaged by mechanical overload.<br />
<br />
Kekurangan motor stepper<br />
- Tingkat efisiensi motor stepper cukup rendah. Motor tetap menyerap tenaga yang besar meskipun bebannya rendah. <br />
- Torsi berbanding terbalik dengan kecepatan, sehingga untuk kecepatan yang tinggi maka torsi yang dihasilkan sangat rendah. <br />
- Memiliki tingkat akurasi yang rendah. Misalnya, 1:200 untuk beban maksimal sedangkan 1:2000 untuk beban yang rendah. <br />
- Cenderung berresonansi atau begetar, oleh karena itu memerlukan Requires microstepping agar dapat bergerak secara halus (<i>smoothly</i>).<br />
- Tidak memerlukan umpan balik untuk mengidentifikasi step yang terlewat (missing).<br />
- Rasio perbadingan torsi terhadap inersia yang tergolong rendah, sehingga tidak dapat menambahkan beban secara cepat. <br />
- Motor dapat menjadi sangat panas saat bekerja pada kemampuan maksimalnya. <br />
- Motor will not "pick up" after momentary overload. <br />
- Motor cenderung bising pada kecepatan menengah hingga kecepatan tinggi. <br />
- Memiliki output tenaga yang rendah dibandingkan ukura dan berat motor. <br />
<br />
Semoga berguna bagi pembaca sekalian. Terima Kasih banyak. <br />
<br />
Daftar Pustaka:<br />
<br />
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<span class="apple-converted-space"><span style="background-color: #dddddd; background-position: initial initial; background-repeat: initial initial;">[1]
Annas, Khairul. 2009. Mengenal Robot. </span></span><span class="apple-style-span"><span style="background-color: #dddddd; background-position: initial initial; background-repeat: initial initial;">23 September
2011, 17:49:59 GMT <a href="http://khairul-annas.blogspot.com/2009/04/mengenal-robot.html"><span style="color: #0000cc;">http://khairul-annas.blogspot.com/2009/04/mengenal-robot.html</span></a></span></span></div>
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[2] Mariss
(from www.geckodrive.com). 2011. Advantages & Disadvantages of Stepper
Motors & DC Servo Motors. 4 Desember 2011, 06:37:24 GMT. <a href="http://www.machinetoolhelp.com/Automation/systemdesign/stepper_dcservo.html">http://www.machinetoolhelp.com/Automation/systemdesign/stepper_dcservo.html</a></div>
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[3] <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 150%;">Science and Technology Studies. 2011.
Perbedaan Motor DC, Motor Stepper, dan Motor Servo. 4 Februari 2011, 23:29 WIB.
</span><a href="http://www.facebook.com/note.php?note_id=162743543775407&comments" style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 150%;">http://www.facebook.com/note.php?note_id=162743543775407&comments</a></div>
skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-56715004970254502432011-05-18T00:11:00.000-07:002012-09-07T05:48:40.739-07:00Kamus Engineering (Inggris - Indonesia)A sound Knowldge : artinya pengetahuan yang matang<br />
<br />
Drum: a cylinder on a revolving shaft, generally for the purpose of driving several pulleys, by means of belts or straps passing around its periphery; also, the barrel of a hoisting machine, on which the rope or chain is wound (7th definition from http://www.definitions.net/definition/drum)skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-70368820437533481082011-04-22T04:10:00.000-07:002012-04-24T13:59:35.622-07:00Amplifier (OP Amp in Instrumentation Amplifier)<div style="text-align: justify;">
<span class="Apple-style-span" style="line-height: 24px;"><a href="http://www.ziddu.com/download/19140566/AMPLIFIER.pdf.html">AMPLIFIER.PDF</a></span></div>
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<span class="Apple-style-span" style="line-height: 24px;"><br /></span></div>
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<span class="Apple-style-span" style="line-height: 24px;">Electrical component/device that used to amplify signal is called amplifier. The Op-Amp is a type of amplifier that common used in many </span><span class="Apple-style-span" style="line-height: 24px;">application. Today we can find the Op-Amp as an IC (<i style="mso-bidi-font-style: normal;">integrated circuit)</i>.</span></div>
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<span class="Apple-style-span" style="line-height: 24px;"></span><span class="Apple-style-span" style="font-weight: bold;"><a href="" name="_Toc287864364">A. Symbol and Modes of Op-Amp</a> circuit</span></div>
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<img alt="" border="0" id="BLOGGER_PHOTO_ID_5598372156148430306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvyyLnPUg6YV-tLHI3UF2MMOJua4IC1G1Np1sHQYgAQc9BCDeEuecKou9YbMsJU4B428rTcd8UD6R_fZRROv1_mgOdSO5JSsFJ7aCqKwHX4NJoo37Qjs9Fm4JEEbli_XyHvpZJrZKF-M1-/s320/%2528Amplifier%2529+Picture+1.jpg" style="cursor: hand; cursor: pointer; display: block; height: 132px; margin: 0px auto 10px; text-align: center; width: 154px;" /></div>
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Picture 1: Symbol of Operational Amplifier </div>
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The circuit symbol for an op-amp is shown above, where:</div>
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V<sub>+ </sub>: non-inverting input</div>
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V<sub>– </sub>: inverting input</div>
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V<sub>OUT </sub>: output</div>
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V<sub>S+ </sub>: positive power supply</div>
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V<sub>S– </sub>: negative power supply</div>
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If we connect the input to the V+, we can get that the output have the same phase with the input. But if we connect the input to the V–, the output will have phase that opposite of the intput phase.</div>
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<span style="color: red;">The power supply pins (and) can be labeled in different ways (See IC power supply pins). Despite different labeling, the function remains the same — to provide additional power for amplification of the signal. Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit</span>.</div>
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<u>Some modes of Op-Amp circuit:<o:p></o:p></u></div>
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<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598372981150162162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly-nvrk0NIfN0KmHbvvtsuKdMVZDT1n_N9V-Kz8bqYGqh_gu-QPQ1XBhYpNaKrnrs8K2kua3cX5gpfpqw9iDCRKbnsBCtEh-Ru2BuuP6kATscjPAudr-KtaKgI8p2LKvLIvw03ldU6VM2/s400/%2528Amplifier%2529+Picture+1abcd.jpg" style="cursor: pointer; display: block; height: 400px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 229px;" /></span></div>
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<br /></div>
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<a href="" name="_Toc287864365"><o:p> </o:p></a></div>
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<o:p> </o:p></div>
<h4 style="margin-left: .25in;">
B.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Development History Op-Amp</h4>
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Op-Amp is a type of differential amplifier. The other type of differential amplifier built from Op-Amp, except the fully differential Op-Amp. The name Operatational Amplifier is used based on the early function that to do some mathematical operational such as summing, difference/subtracting, intregration, or differential.</div>
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Op-Amp terdiri atas beberapa jenis, yaitu:</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1941: First (vacuum tube) op-amp<o:p></o:p></u></div>
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The first op-amp design for a general-purpose, DC-coupled, high gain, inverting feedback amplifier. This design used three vacuum tubes to achieve a gain of 90 dB and operated on voltage rails of ±350 V. It had a single inverting input rather than differential inverting and non-inverting inputs, as are common in today's op-amps. </div>
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It is found in U.S. Patent 2,401,779 "Summing Amplifier" filed by Karl D. Swartzel Jr. of Bell labs in 1941. This design proved its value by being liberally used in the M9 artillery director. The artillery director worked with the SCR584 radar system to achieve extraordinary hit rates (near 90%) that would not have been possible otherwise. [Jung, Walter G. (2004). "Chapter 8: Op Amp History". Op Amp Applications Handbook. Newnes. p. 777]</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1947: First op-amp with an explicit non-inverting input<o:p></o:p></u></div>
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In 1947, the name of Operational Amplifier is first formally defined in a paper by Professor John R. Ragazzini, a professor from Columbia University. In the paper a footnote, Ragazzini mentioned that the op-amp design by Loebe Julie (one of his student) would turn out to be quite significant. This op-amp was superior in a variety of ways, but its had two major innovations. The first is input stage used a long-tailed triode pair with loads matched to reduce drift in the output. Second, that more importantly, was the first op-amp design to have two inputs (one inverting, the other non-inverting). This differential input made a whole range of new functionality possible, but it would not be used for a long time due to the rise of the chopper-stabilized amplifier.[ Jung, Walter G. (2004). "Chapter 8: Op Amp History". Op Amp Applications Handbook. Newnes. p. 779]</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1949: First chopper-stabilized op-amp<o:p></o:p></u></div>
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In 1949, Edwin A. Goldberg designed a chopper-stabilized op-amp.[ Jung, Walter G. (2004). Op Amp Applications Handbook. Newnes]. <span style="color: black;">The chopper gets an AC signal from DC by switching between the DC voltage and ground at a fast rate (60 Hz or 400 Hz). The advantage of this Op-Amp was improved the gain while significantly reducing the output drift and DC offset. Unfortunately, any design that used a chopper couldn't use their non-inverting input for any other purpose. Techniques that used the non-inverting input regularly would not be popular until the 1960s when op-amp ICs started to show up in the field.</span></div>
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Picture 2: GAP/R’s K2-W Vacume tube op-amp</div>
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In 1953, vacuum tube op-amps produced commercially. The op-amp available in the K2-W model and K2-P (chopper add-on available that would effectively eliminate the non-inverting input). The vacume tube op-amp was based on Loebe Julie's (1947) design of op-amp and. This commercially op-amp would start the widespread use of op-amps in industry.</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1961: First discrete IC op-amps<o:p></o:p></u></div>
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The birth of transistor in 1947 and silicon transistor in 1954 has made “the dream” of Integrated Circuits (ICs) became a reality. Planar process introduced in 1959 made transistor and ICs stable enough to be commercially useful. Then GAP/R's model P45 (solid-state, discrete op-amps) were being produced in 1961.</div>
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Picture 3: GAP/R's model P45 (solid-state, discrete op-amps in 1961)</div>
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<span style="color: red;">These op-amps were effectively small circuit boards with packages such as edge-connectors. They usually had hand-selected resistors in order to improve things such as voltage offset and drift. The P45 (1961) had a gain of 94 dB and ran on ±15 V rails. It was intended to deal with signals in the range of ±10 V.<o:p></o:p></span></div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1962: First op-amps in potted modules<o:p></o:p></u></div>
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Picture 4: GAP/R's model PP65 (a solid-state op-amp in a potted module)</div>
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The op-amp circuit became more generally use in many industry and many device. Several companies were try to made the op-amp into a single black box so it could be easily threated as a single component. One of the result, in 1962, was GAP/R's model PP65, a solid-state op-amp in a potted module.</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1963: First monolithic IC op-amp<o:p></o:p></u></div>
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<span style="color: black;">In 1963, the first monolithic IC op-amp, the μA702 designed by Bob Widlar at Fairchild Semiconductor, was released. Monolithic ICs just a single piece of chip. Its is different from a chip and discrete parts (a discrete IC), or multiple chips bonded and connected on a circuit board (a hybrid IC). Almost all modern op-amps are monolithic ICs; however, this first IC did not meet with much success. Some problem such as an uneven supply voltage, low gain and a small dynamic range held off the dominance of monolithic op-amps. But the problems had been solved in 1965, when the μA709 (also designed by Bob Widlar) was produced.<o:p></o:p></span></div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1966: First varactor bridge op-amps<o:p></o:p></u></div>
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<span style="color: red;">Since the 741, there have been many different directions taken in op-amp design. Varactor bridge op-amps started to be produced in the late 1960s. They were designed to have extremely small input current and are still amongst the best op-amps available in terms of common-mode rejection with the ability to correctly deal with hundreds of volts at their inputs.<o:p></o:p></span></div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1968: Release of the μA741<o:p></o:p></u></div>
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Further improvement in monolithic op-amp result in release of the LM101 in 1967, which solved a variety of issues. This is followed by the μA741 in 1968. The μA741 was extremely similar to the LM101, except that Fairchild's facilities allowed them to include a 30 pF compensation capacitor inside the chip. so it didn’t required external compensation. This simple difference has made the 741 as a legendary op-amp and many modern amplifiers base their pinout on the 741’s. The μA741 is still in production, and has become ubiquitous in electronics — many manufacturers produce a version of this classic chip, recognizable by part numbers containing 741.</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1970: First high-speed, low-input current FET design<o:p></o:p></u></div>
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After 741 the derection of improvement were focus high speed and low-input current design. The design started to be made by using FETs, however, it would be largely replaced by op-amps made with MOSFETs in the 1980s. During the 1970s single sided supply op-amps also became available.</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>1972: Single sided supply op-amps being produced<o:p></o:p></u></div>
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A single sided supply op-amp is one where The input and output voltages of a single sided supply can be as low as the negative power supply. This make the op-amp can operate in many applications with the negative supply pin being connected to the signal ground. It was eliminating the need for a separate negative power supply.</div>
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In 1972, the LM324, one such op-amp that came in a quad package (four separate op-amps in one package), was released and became an industry standard As the properties of monolithic op-amps improved, the more complex hybrid ICs were quickly relegated to systems that are required to have extremely long service lives or other specialty systems.</div>
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-<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><u>Recent trends<o:p></o:p></u></div>
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Recently supply voltages in analog circuits have decreased (near voltages they have in digital logic) and low-voltage op-amps have been introduced reflecting this. Supplies of ±5 V and increasingly 5 V are common. The modern op-amp signal can range from lowest supply voltages to the highest, either input or output.</div>
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<a href="" name="_Toc287864366">C.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Ideal Op-Amp</a></h4>
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An ideal op-amp is usually considered to have the following properties, and they are considered to hold for all input voltages:</div>
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a.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Infinite open-loop gain (when doing theoretical analysis, a limit may be taken as open loop gain A<sub>OL</sub> goes to infinity); </div>
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b.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Infinite voltage range available at the output, V<sub>out</sub>. In practice the voltages available from the output are limited by the supply voltages V<sub>S+</sub> and V<sub>S– </sub>. The power supply sources are called rails.</div>
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c.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Infinite bandwidth (i.e., the frequency magnitude response is considered to be flat everywhere with zero phase shift).</div>
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d.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Infinite input impedance (so, in the diagram, R<sub>in</sub> = ∞, and zero current flows from v<sub>+</sub> to v<sub>–</sub>).</div>
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e.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Zero input current (i.e., there is assumed to be no leakage or bias current into the device).</div>
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f.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Zero input offset voltage (i.e., when the input terminals are shorted so that v<sub>+</sub> = v<sub>–</sub>, the output is a virtual ground or v<sub>out</sub> = 0).</div>
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g.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Infinite slew rate (i.e., the rate of change of the output voltage is unbounded) and power bandwidth (full output voltage and current available at all frequencies). </div>
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h.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Zero output impedance (i.e., R<sub>out</sub> = 0, so that output voltage does not vary with output current).</div>
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i.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Zero noise.</div>
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j.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Infinite Common-mode rejection ratio (CMRR).</div>
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k.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Infinite Power supply rejection ratio for both power supply rails.</div>
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All of this ideals can be summarized by the two "<b style="mso-bidi-font-weight: normal;">golden rules</b>":</div>
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I. <span class="Apple-style-span" style="line-height: normal;">The output attempts to do whatever is necessary to make the </span><span class="Apple-style-span" style="line-height: normal;">voltage </span><span class="Apple-style-span" style="line-height: normal;">differen</span><span class="Apple-style-span" style="line-height: normal;">ce</span></div>
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<span class="Apple-style-span" style="line-height: normal;"> between the inputs zero. </span><span class="Apple-style-span" style="line-height: normal;"><span style="font-family: Wingdings;">à</span></span><span class="Apple-style-span" style="line-height: normal;"> (V</span><span class="Apple-style-span" style="line-height: normal;"><sub>+</sub></span><span class="Apple-style-span" style="line-height: normal;"> – V</span><span class="Apple-style-span" style="line-height: normal;"><sub>–</sub></span><span class="Apple-style-span" style="line-height: normal;"> = 0 or V</span><span class="Apple-style-span" style="line-height: normal;"><sub>+</sub></span><span class="Apple-style-span" style="line-height: normal;"> = V</span><span class="Apple-style-span" style="line-height: normal;"><sub>–</sub></span><span class="Apple-style-span" style="line-height: normal;"> ) </span></div>
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<span class="Apple-style-span" style="line-height: normal;"> This rule only applies in the usual case where the op-amp is used as inverting design (negative feedback). These rules are commonly used as good first approximation for analyzing or designing op-amp circuits.</span></div>
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II.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>The inputs draw no current. <span style="font-family: Wingdings;">à</span> (i<sub>+</sub> = i<sub>–</sub> = 0). </div>
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The real is none of these ideals can be perfectly realized, <span style="color: red;">and various shortcomings and compromises have to be accepted. Depending on the parameters of interest, a real op-amp may be modeled to take account of some of the non-infinite or non-zero parameters using equivalent resistors and capacitors in the op-amp model. The designer can then include the effects of these undesirable, but real, effects into the overall performance of the final circuit. Some parameters may turn out to have negligible effect on the final design while others represent actual limitations of the final performance, that must be evaluated.</span></div>
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<o:p> </o:p></div>
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D.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>Basic Design Circuit with Op-Amp for Amplifier</h4>
<ol start="1" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l9 level1 lfo6; text-align: justify;"><i style="mso-bidi-font-style: normal;">Inverting Amplifier<o:p></o:p></i></li>
</ol>
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It is called inverting amplifier because the design connect the input to the inverting pin of the Op-Amp.</div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: center;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598374983540441650" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGAd5ZEtHscnBNJxC-LGWJ1jUqnZeVRFpRWogN2jjTNpFInBvJH9sD7Vlurds27jSZBThV5trM_yIwTLPNXR_SzEMM_tFbxZiqvVhN4Axcp3dJwMz9zTkE_N_vV0r5nO_9QKuiUYycyq6h/s320/%2528Amplifier%2529+Picture+5.jpg" style="cursor: pointer; display: block; height: 186px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: center;">
<i style="mso-bidi-font-style: normal;">Picture 5: Schematic of inverting amplifier<o:p></o:p></i></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
We can analized the scheme above using the golden rule to get the value of amplification. </div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .75in; mso-list: l3 level1 lfo8; text-align: justify; text-indent: -.25in;">
I.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>V<sup>*</sup> = 0 or V<sub>+</sub> = V<sub>– </sub>, because of V<sub>+</sub> connect to the ground so: V<sub>+</sub> = V<sub>– </sub>= 0</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .75in; mso-list: l3 level1 lfo8; text-align: justify; text-indent: -.25in;">
II.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><i style="mso-bidi-font-style: normal;">i</i><sub>+</sub> = <i style="mso-bidi-font-style: normal;">i</i><sub>–</sub> = 0</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
<span class="Apple-style-span" style="line-height: normal;">From the kirchoff law’s <i style="mso-bidi-font-style: normal;">i<sub>1</sub> + i<sub>2</sub> = i <sub>–</sub></i> ,so:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
<span class="Apple-style-span" style="line-height: normal;"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598405078635102626" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqk9SEP5Jh8EEffEqRsppDFCYtuhZYSJz4AlsmDcs4ggSiYVWjnBJAr4ou6ZytnAHROif2daruftYHmBaik7kMSGccBCElLzTKxurwq8f18xkbT4BbItgNBHDFwYM5EmpKDSrdIoz6iZIj/s400/%2528Amplifier%2529+Equation+3.jpg" style="cursor: pointer; display: block; height: 29px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 244px;" /></span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598404851120483906" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9iS5DTZL93ZrwZERK-8OHcwYQloqqaxqFS-0iKWOjbY8cyK7MlMw4Me5kZ2W1ygTuIxHrM1_1GqU5vZgvy7tKlHcrd8DPtU0zrq6NQi6CMhK6Cp80rJiXuXThrn7Qrm0Z6hDBB25noCU3/s400/%2528Amplifier%2529+Equation+4%252C5.jpg" style="cursor: pointer; display: block; height: 110px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
<div>
<div style="text-align: center;">
<span class="Apple-style-span"><br /></span></div>
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
Insert equation 4 and 5 into equation 3 we can get the relation of the input and the output voltage, as a function of the resistances:</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598404226643548434" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsLsA3l3_bAy2Yz4vMzJpwYrMvpfe5lsTp8ASkzHDiX1YvsRT5fxd5IGlEPhK5Gd4EIw5V25iIs1QHYbC1BXo6ysEwAZS-nAcY0UcAk7MBOqbJ45Y1U1VSDyfhM60V6b1gr4Efq218a8sy/s400/%2528Amplifier%2529+Equation+6.jpg" style="cursor: pointer; display: block; height: 52px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 369px;" /></span></div>
<ol start="2" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l9 level1 lfo6; text-align: justify;">Non-Inverting Amplifier</li>
</ol>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: center;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598403961619315010" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaC8vb_MdnwTSzhH2sPckb3KVVyXi6xFmGlGZYkZntjrFk-FezP-xnActna7cMhlXsPQVvuPgcKE3m-AISwzonbIWhxPbbbQcuCjp5KDXBrIGJ_Bkunnz3m_dHMKvvAQjCyfVQK-VXgcH9/s400/%2528Amplifier%2529+Picture+6.jpg" style="cursor: pointer; display: block; height: 163px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 321px;" /></span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: center;">
<i style="mso-bidi-font-style: normal;">Picture 6: Schematic of non-inverting amplifier<o:p></o:p></i></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
As same as non-inverting amplifier, we can analized the scheme above using the golden rule to get the value of amplification. </div>
<div class="MsoListParagraphCxSpFirst" style="line-height: 150%; margin-left: .75in; mso-add-space: auto; mso-list: l11 level1 lfo14; text-align: justify; text-indent: -.25in;">
I.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>V<sup>*</sup> = 0 or V<sub>+</sub>=V<sub>– </sub>, because of V<sub>+</sub> connect to the source so: V<sub>–</sub> = V<sub>+ </sub>= V<sub>i </sub></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-left: .75in; mso-add-space: auto; mso-list: l11 level1 lfo14; text-align: justify; text-indent: -.25in;">
II.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><i style="mso-bidi-font-style: normal;">i</i><sub>+</sub> = <i style="mso-bidi-font-style: normal;">i</i><sub>–</sub> = 0, so all of the current flowing through R<sub>2</sub> also flowing through R<sub>1</sub>. Therefore, R<sub>2</sub> and R<sub>1</sub> can be approximated such voltage devider circuit as shown by the scheme below:</div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .75in; margin-right: 0in; margin-top: 0in; text-align: center;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598403542016200098" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFA3trWAVdyDwLpD05j6Vl3k5K4U1j4NxbJpOJJbkE1LtxloAMrFj-9xWXKzcmUEfM-xR_w7W19hV-OOAd4fWjiYsemczWuMqkfbpjdfwj-WgBAR7Yk3OOe9B4o16kN8iebjbR_ct-QU7x/s400/%2528Amplifier%2529+Picture+7.jpg" style="cursor: pointer; display: block; height: 218px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 290px;" /></span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt; text-align: center;">
<i style="mso-bidi-font-style: normal;">Picture 7: Schematic of voltage devider<o:p></o:p></i></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-align: justify;">
Now we can use the voltage devider as shown in the equation below:</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-align: justify;">
<span class="Apple-style-span" style="line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598403377032530722" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgifL5aYQNjQSTpzl2i14q5i6_EsEyCtxJ9uWi0Oek2XdYCrcvf5lmN0U4OkXzFvjtxBo3aWU-vbqOf96Y118iVheZHSxiDMJhOEFWRqBS80YUARKivoSuraApRviiZ-LJxb-cXpdQs9zNN/s400/%2528Amplifier%2529+Equation+7.jpg" style="cursor: pointer; display: block; height: 37px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-align: justify;">
As we know in the first rule, so the output voltage are:</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-align: justify;">
<span class="Apple-style-span" style="line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598403242486112626" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8QI8i9wCI_Ba07Sai6QnSd1TA08tFQQNpkHyU-YYUuw-jUJofJ_WyEsbSI8Lpzv5otVPIUteFoG62px2SsvSMem5dT5cgqH1PHwwp2Y7PWK41ezg6byH8HI0e07x_n6_yZ1d2ljvJ3tK9/s400/%2528Amplifier%2529+Equation+8.jpg" style="cursor: pointer; display: block; height: 49px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: 81.0pt; margin-right: 0in; margin-top: 0in; text-align: justify;">
</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: 81.0pt; margin-right: 0in; margin-top: 0in; text-align: justify;">
<o:p> </o:p></div>
<ol start="3" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l9 level1 lfo6; text-align: justify;">Voltage / unity follower<i style="mso-bidi-font-style: normal;"><o:p></o:p></i></li>
</ol>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: center;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598401373370380082" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxHEN-Ekq2qWVVdNQKjJ9S4P3_MxB1OHHllhwufwBaHaywdtMIDsggneh1t2BDMsMAbWiVcXzeFjZngZEyJsY1BU4zwuqW0_oIE5ywbuj1PhCnAo20qX03PgwRoXlnxtNRamn5PiYeuQ2S/s400/%2528Amplifier%2529+Picture+8.jpg" style="cursor: pointer; display: block; height: 160px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 249px;" /></span></div>
<div>
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><br /></span></div>
<div class="Gambar" style="text-align: center;">
Picture 8:<span style="font-style: normal;"> </span>Voltage Follower</div>
<br />
The voltage follower, also known as a pre-amplifier, is a unity gain amplifier circuit with a short circuit in the feedback path, as shown in Figure 5.16, such that:<br />
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-margin-bottom-alt: auto; text-align: center;">
<span class="Apple-style-span" style="line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598401038734314162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbyJ5NAwbiJDTd2C2x0F3U3Ipe8l0xQ2lG850R89uJlANv_nJT3JJ5MK9PBnZ9HDU1PKZCczfTNGCkAiJFJEtiqo9F6XlcJuleGv20jx6EjrVUhgc8GC4_mPVjvTeqxkdZj5Q610vJ20GR/s400/%2528Amplifier%2529+Equation+9.jpg" style="cursor: pointer; display: block; height: 29px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 337px;" /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-margin-bottom-alt: auto; text-align: justify;">
It has a very high input impedance and its main application is to reduce the load on the measured system. It also has a very low output impedance that is very useful in some impedance-matching applications.</div>
<ol start="4" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l9 level1 lfo6; text-align: justify;">Common Mode</li>
</ol>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
Figure 5.12 shows a common amplifier configuration that is used to amplify the small difference that may exist between two voltage signals V<sub>A</sub> and V<sub>B</sub>. These may represent, for example, the pressures either side of an obstruction device put in a pipe to measure the volume flow rate of fluid flowing through it. The output voltage 0 is given by:</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt; text-align: justify;">
</div>
<div style="text-align: -webkit-auto;">
<span class="Apple-style-span"><span class="Apple-style-span" style="font-size: 15px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598399286735327074" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV9WmtBPtzX1es2y9TKMOqfJ6npu5NoICutcTU8m6jul7YQqIWfF7eWldUVJytrw6_IHmLekizFeleL8h0M6UFgaiKHspSUKoFTYEqIe0Ll9oQvQCF4UVABbp4P00DF8noq_TYjxSDUbcY/s400/%2528Amplifier%2529+Equation+10.jpg" style="cursor: pointer; display: block; height: 46px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
A differential amplifier is also very useful for removing common mode noise voltages. Suppose V<sub>A</sub> and V<sub>B</sub> in Figure 5.12 are signal wires such that V<sub>A </sub>= +Vs volts and V<sub>B</sub> = 0 volts. Let us assume that the measurement circuit has been corrupted by a common mode noise voltage Vn such that the voltages on the +Vs and 0V signal wires become (Vs + Vn) and (Vn). The inputs to the amplifier V<sub>1</sub> and V<sub>2</sub> and the output V<sub>0</sub> can then be written as:</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
<span class="Apple-style-span" style="line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598398862200260162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju6LA3NLq4ip1aXVxGMMpn_cpp1rtChIAlIXcJl-s64FnV3fx0UaFOut6gVW3l63x9GQ0TrDyMDkz2pSbw6ZFgKZZf1O467wf4CT-nW1_q6e7l8ST-J2bnjBGPxQHI49yTV0EkcCQCM6W3/s400/%2528Amplifier%2529+Equation+10a.jpg" style="cursor: pointer; display: block; height: 98px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 149px;" /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
So the output will be:</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598398263653837586" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4jLFMolHYmYR6SBqCbNcAwknseou64Y0YkF69oP9y2_rt9ppaIXb7EBheJuQ1PD_unMOFd39BzeAnNdaJ8sJOCMG9bfCUK41PJodAGrJMFJfUk7eLyNjbWACF9-MErxDtuzLnmyGPp2cg/s400/%2528Amplifier%2529+Equation+11.jpg" style="cursor: pointer; display: block; height: 43px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598398063852879970" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcIvc_ZU_Ce4-4aepsynfuuuzdU5WJNChx0t6JdYLW0adqpB8OX_H3yJx21N7_BHGJVx-USLs3VAzAMLXTfUAbZx9WK3bn-zEXLvHie_2FebmSbO6CSYAIzT_1ty5bkFM4T6lvw5YsUJ4i/s400/%2528Amplifier%2529+Picture+8b.jpg" style="cursor: pointer; display: block; height: 186px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
<div>
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
Hence:</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: 63.0pt; margin-right: 0in; margin-top: 0in; text-align: justify;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: 63.0pt; margin-right: 0in; margin-top: 0in; text-align: justify;">
</div>
<div class="MsoNormal" style="margin-bottom: 6pt; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-align: -webkit-auto;">
<span class="Apple-style-span"><span class="Apple-style-span" style="font-size: 15px;"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598397121620605506" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggFJopvLI_q18pzoctqr7an-TdZ_ldwgOX89AzPEiwqY6CHfjOT5zCdd81xXuW45VUENP2d-L-WjTX39cdWrb4YJkY55mPDmdcYsormeeykocBE_FAg6BNLGcDmaTe34vBNmx3ccdTSinD/s400/%2528Amplifier%2529+Equation+12.jpg" style="cursor: pointer; display: block; height: 173px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></span></span></div>
<div class="MsoNormal" style="margin-bottom: 6pt; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-align: -webkit-auto;">
</div>
<div style="text-align: left;">
If the resistance value are chosen carefully such that R<sub>4</sub>/R<sub>2</sub> = R<sub>3</sub>/R<sub>1</sub>, then the equation above simplifies to:</div>
<div class="MsoNormal" style="margin-bottom: 6pt; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-align: -webkit-auto;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598396763926049106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6dzYiLYDoSIyrUYpD0FR89sj7SvAD2vL3y_UwetYEx26jJT_tQjYgjN5h5XXD9E2s0sTFTSfip2KnRbWKwn3dvtt-fX2m7wCNq3Aon8d06h6zjpLYMhTiqWNrRCgZQ7lz77KPv3_XNQjR/s400/%2528Amplifier%2529+Equation+13.jpg" style="cursor: pointer; display: block; height: 43px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
<div class="MsoNormal" style="margin-bottom: 6pt; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-align: -webkit-auto;">
<span class="Apple-style-span"><span class="Apple-style-span" style="font-size: 15px;"></span></span>In this example, the voltage noise has been removed (Alan S. Morris. 2001. <i style="mso-bidi-font-style: normal;">Measurement and Instrumentation Principles</i>, Third Edition. Butterworth-Heinemann). But in the real case we can’t make the R<sub>4</sub>/R<sub>2</sub> perfectly the same as R<sub>3</sub>/R<sub>1</sub>, we just make both fraction value near each other. The output of a real differential amplifier is better described as:</div>
<div>
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<o:p> </o:p></div>
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<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598395306470119394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIBwFs1syfsmM4a9Z3LeA_ZtsKW7eFOqt370XHZ6tO47NbRIB4pY_GdxOXcVTiX2pcCjR0G-NKf6U0eMQ10CpL343a6S2Hd8ljjtnLLU0kVNMR9cs67I4TYPuVc9Wckq6OARxemmxuOYKS/s400/%2528Amplifier%2529+Equation+14.jpg" style="cursor: pointer; display: block; height: 38px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
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where A<sub>cm</sub> is the common-mode gain or the gain of noice, which is typically much smaller than the differential gain A<sub>d</sub>.</div>
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<br />The CMRR is defined as the ratio of the powers of the differential gain over the common-mode gain, measured in positive decibels (thus using the 20 log rule):</div>
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<span class="Apple-style-span" style="line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598394749731557074" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA62nj_-CfihuKb3LDtuLt-chyphenhyphen3JI7jWaTwGX47SB1E-y8HVTFpsovdMu6sGQfqJ8I2NLJgv_tdtucJejThRNHyHXdXynL1Y7uLE2sMVMqpNdTlXo-MOrqI-K3StX4sAwuFBIDIW61ocRJ/s400/%2528Amplifier%2529+Equation+15.jpg" style="cursor: pointer; display: block; height: 57px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 397px;" /></span></div>
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<o:p> </o:p></div>
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The CMRR is a very important specification, as it indicates how much of the common-mode signal will appear in your measurement. The value of the CMRR often depends on signal frequency as well, and must be specified as a function there of. </div>
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It is often important in reducing noise on transmission lines. For example, when measuring the resistance of a thermocouple in a noisy environment, the noise from the environment appears as an offset on both input leads, making it a common-mode voltage signal. The CMRR of the measurement instrument determines the attenuation applied to the offset or noise (<a href="http://en.wikipedia.org/wiki/Common-mode_rejection_ratio">http://en.wikipedia.org/wiki/Common-mode_rejection_ratio</a>, 11<sup>th</sup> April 2011. 10:38 PM). </div>
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<span class="Apple-style-span" style="font-weight: bold; line-height: normal;"><a href="" name="_Toc287864367">E.O</a>perational and Other Design Circuit with Op-Amp</span></div>
<ol start="1" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l2 level1 lfo7;">Summing <i style="mso-bidi-font-style: normal;">amplifier</i></li>
</ol>
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<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598393916838406786" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheLBt-tmuKS55j1CjT6CZRAbIeKSk1q-kijzxufCHSUPJzOPjiFXKzdpFeKaaCkmtBRFmkvyz0tUVh4K36p18LCWcS4ls7gUYBORXnVdaOy9RDi2Sr8pPNVmryN_pnH_AVDhC8IzXN_Yjg/s400/%2528Amplifier%2529+Picture+9.jpg" style="cursor: pointer; display: block; height: 156px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
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<i style="mso-bidi-font-style: normal;">Picture 9: Summing amplifier<o:p></o:p></i></div>
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From the golden rule:</div>
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I.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>V<sup>*</sup> = 0 or V<sub>+</sub>=V<sub>– </sub>, because of V<sub>+</sub> connect to the ground so: V<sub>–</sub> = V<sub>+ </sub>= 0</div>
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II.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><i style="mso-bidi-font-style: normal;">i</i><sub>+</sub> = <i style="mso-bidi-font-style: normal;">i</i><sub>–</sub> = 0, so </div>
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<o:p> </o:p></div>
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<span style="font-family: 'Times New Roman', serif;"><span class="Apple-style-span">And from kirchoff’s law, we know that the current enter point A is the same as the current leave that point.</span></span></div>
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<span style="font-family: 'Times New Roman', serif;"><span class="Apple-style-span"><span class="Apple-style-span" style="font-family: Georgia, serif; font-size: 15px; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598393701887094706" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj81IGyvM0zLjuQp_AxtdKntNWwuHSj_w-_pShyFms1ylNed0sYS1bSCvWhDYswgvjW8sK1dlJ5NQK21mJJVXqiMPFYlp8Y8xqhO_dbRfr1CK2Kq_1nS0CZyOEnJjj1R0Ngbm-09-8tWhDm/s400/%2528Amplifier%2529+Equation+16.jpg" style="cursor: pointer; display: block; height: 36px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 382px;" /></span></span></span></div>
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Insert the voltage devider, the equation above can be write as:</div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<img alt="" border="0" id="BLOGGER_PHOTO_ID_5598392704947445986" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN5T51Dzml6z02Y9ta4paAvZCrJmxciUNyfPe_HXrRCycTZeXYofESRFi7C4vhnwpCpX-kzUhJ1Hw7aQBBnPZSKUKeUxYt2EaWGxnbcmmvfuDYdpWWN0g2ThqRsQggeH4KLdOrkNrVx1fZ/s400/%2528Amplifier%2529+Equation+16a.jpg" style="cursor: pointer; display: block; height: 50px; line-height: normal; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 218px;" />Based on the golden rule, we can approximate the equation as:</div>
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<o:p> </o:p></div>
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</div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598392444773710610" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXBhaIg1K5lSuTXc0hbVUpudxYurk9eQ_xjQxKcWM9wJAJekTqVNjJ7EGbNpDBe_6IysHB5oLcFz38bV0hVgIdFdGQsilrTMuNhxrcHxo_QtMJc4qiQhsEA4NvJvaVYs67CliqPvu8ur2G/s400/%2528Amplifier%2529+Equation+17.jpg" style="cursor: pointer; display: block; height: 90px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></span></div>
<div>
<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><br /></span></span></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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Special case:</div>
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<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span>If we assume or make the <i style="mso-bidi-font-style: normal;">R<sub>1</sub>=R<sub>2</sub>=R<sub>n</sub>=R</i>, where <i style="mso-bidi-font-style: normal;">R<sub>n</sub></i> and <i style="mso-bidi-font-style: normal;">V<sub>n</sub></i> connect to the point A the fuction of output voltage is:</div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598392188301451490" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZvD3W36XSta6jI2eiY0Mi0Tun6Y_SkW_HfaOe7Ifm62x6Mihn4ihoa-bkxFmEVTWIbxISuOCQGierMSxKqFjPcZxY1TwQEAfj6dD60HqJldD0IStZtKg0i9zYuDlt6gh8juaTrE1CGZMu/s400/%2528Amplifier%2529+Equation+18.jpg" style="cursor: pointer; display: block; height: 46px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 334px;" /></span></span></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
<ol start="2" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l2 level1 lfo7;">Subtractor / Diferential amplifier</li>
</ol>
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This is the combining of inverting and non-inverting design of operational amplifiers. All the input connect to the inverting pin will subtract all the input that connect to the non-inverting pin. This in because the inverting pin will produce the inverted output signal from all sources connect to the pin.</div>
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<o:p> </o:p></div>
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<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598389674545230434" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQqD0lXp0kHjMxOuCGnttrqLk-feB373qxNXdjh_EB8rvoHkkx3fjjnj2KVIdEQYc4TEP4HbdfT0BrjC5HTXjGxl-yeTZ2LbQZj3CD8GPZ7yEePQ_2g-PJpm33qLX2J13URV0av6aHNgsK/s400/%2528Amplifier%2529+Picture+10.jpg" style="cursor: pointer; display: block; height: 221px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></div>
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<i style="mso-bidi-font-style: normal;">Picture 10: Scheme of subtractor/diferential amplifier <o:p></o:p></i></div>
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From the golden rule:</div>
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I.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>V<sup>*</sup> = 0 or V<sub>+</sub>=V<sub>–</sub></div>
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II. <span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><i style="mso-bidi-font-style: normal;">i</i><sub>+</sub> = <i style="mso-bidi-font-style: normal;">i</i><sub>–</sub> = 0, so</div>
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We can get two more equation. First is the equation for inverting side:</div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598389329554556034" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisMLaFPPPM1Y-0mbkwRg9mpP6pL66dB3CdQJ_ETiMNmrnIj4w_mt7sD7_y1ppVGGwXF8C8OEKtcoNv3GM0wVF5xdAI1P8L1tnClnalgzJLPt9CEcS_YR8XuEacop1li9mpBrLtT6rJ1ut4/s400/%2528Amplifier%2529+Equation+19.jpg" style="cursor: pointer; display: block; height: 164px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></span></span></div>
<div>
<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><br /></span></span></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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The second equation is for the non-inverting side, that can be approximate as the voltage devider.</div>
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</div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598389112464140418" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl1vEcg9N3J5buF9vQHWvb23OxJwC2C9Gk_tEgXMcy5Y0ik6DG8FiS6YJjk3P8rZJdy9xNJnd4bW1b7SxKQZSOByq6hKx64Y1V5ac4LlJ9QAE6ebpxaUMN9pLtLJImapzFavR18ORH51jQ/s320/%2528Amplifier%2529+Equation+20.jpg" style="cursor: pointer; display: block; height: 42px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></span></div>
<div>
<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><br /></span></span></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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Using the first rule of golden rule we can combine this two equation (equ.19 and equ. 20) as:</div>
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</div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598388508227588306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnTszb1-p20-zRyLOX7YiwaU4_ONODbNi9F7KzwQUrIfnYDmFNrQ032Gv6VUq-6I9SdHE6_KuznYrBMDa3qegH71p2PppHzI7_eVTp6FsQBxTggOAiQbg0oiD2R7fwvwH6ZqJIoKnCXoF-/s320/%2528Amplifier%2529+Equation+21.jpg" style="cursor: pointer; display: block; height: 41px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></span></div>
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For a special case where the <span class="Apple-style-span" style="font-family: 'Times New Roman', serif; line-height: normal;">R<sub>g</sub>/R<sub>2</sub>=R<sub>f</sub>/R<sub>1</sub>=K</span>, the equation can be simplify:</div>
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<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598388125556546546" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfsrQEYcOOXVKXiKDBRixo80m1me90_khiYP54FMQ9pMJeZCk7eJygywkBb7opRCp1qHlz0EpTHr1DScomZ5lneS92b8UsRIbT9V8Jh1rma80Tn2CHAEHN2fmzX3EaLsI8gb2A3GnhD01J/s320/%2528Amplifier%2529+Equation+22.jpg" style="cursor: pointer; display: block; height: 136px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></span></div>
<div>
<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 15px;"><br /></span></span></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<ol start="3" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l2 level1 lfo7;">Differentiator</li>
</ol>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
The basic of analizing this circuit is using the golden rule.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .75in; mso-list: l1 level1 lfo12; text-align: justify; text-indent: -.25in;">
I. <span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>V<sup>*</sup> = 0 or V<sub>+</sub> = V<sub>– </sub>, because of V<sub>+</sub> connect to the ground so: V<sub>+</sub> = V<sub>– </sub>= 0</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .75in; mso-list: l1 level1 lfo12; text-align: justify; text-indent: -.25in;">
II.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><i style="mso-bidi-font-style: normal;">i</i><sub>+</sub> = <i style="mso-bidi-font-style: normal;">i</i><sub>–</sub> = 0</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63pt; text-align: center;">
<img alt="" border="0" id="BLOGGER_PHOTO_ID_5598386547873304898" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFE9BHv-IcV5ogkT9OdknywhV-NVVzCCXi0kxHHo_WqGdkywVHJWag8PeAqccFonQmC3RW3M5yiyMP-NkPO5ajKv47d20qMQnHMedUNweD5P3WjtMTx7SnZz0OaeNHW_T72ptrZi9vZao4/s320/%2528Amplifier%2529+Picture+11.jpg" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; cursor: pointer; display: block; height: 154px; line-height: normal; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></div>
<div class="Gambar" style="text-align: center;">
Picture 11: Differentiator Amplifier</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in;">
<span style="height: 33px; left: 0px; margin-left: 517px; margin-top: 27px; position: absolute; width: 84px; z-index: 15;"> </span></div>
<table cellpadding="0" cellspacing="0"> <tbody>
<tr> <td height="33" style="vertical-align: top;" width="84"><span style="left: 0pt; position: absolute; text-align: right; z-index: 15;"><br /></span> </td> </tr>
</tbody></table>
<span class="Apple-tab-span"></span><br />
<div style="text-align: justify; white-space: pre;">
<span class="Apple-tab-span"><span class="Apple-style-span" style="white-space: normal;"><span class="Apple-tab-span" style="white-space: pre;"> </span>From the kirchoff's law, we can get:</span></span></div>
<div style="text-align: justify; white-space: pre;">
<span class="Apple-tab-span"><span class="Apple-style-span" style="white-space: normal;"><br /></span></span></div>
<div style="text-align: justify; white-space: pre;">
<span class="Apple-tab-span"><span class="Apple-style-span" style="white-space: normal;"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598386128200299458" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-7ElDvRZ7YOfVfbK3vXgfmtiHP5w1pCFlQnDcT3B4_t6w-PIaTosRWCHjoCjgIuKpn4SWXm-bnmyVEHWOHFzfmrkUoc9IKR20o3xG20n2VmD2sSMl3jjKzexYMVxDOu8BcX-oSQM_8SoY/s320/%2528Amplifier%2529+Equation+23.jpg" style="cursor: pointer; display: block; height: 34px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></span></span></div>
<div>
<span class="Apple-tab-span"><span class="Apple-style-span"><br /></span></span></div>
<br />
<div>
<table align="left" cellpadding="0" cellspacing="0"><tbody>
<tr><td><span class="Apple-tab-span" style="white-space: pre;"> </span>U</td><td style="text-align: justify;"><span class="Apple-style-span" style="font-size: 16px; line-height: 24px;">sing the golden rule:</span></td></tr>
</tbody></table>
<div style="text-align: -webkit-auto;">
<span class="Apple-style-span"><br /></span></div>
<div style="text-align: -webkit-auto;">
<span class="Apple-style-span"><br /></span></div>
<div style="text-align: -webkit-auto;">
<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 16px;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598382696768360306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXowvSo_kP7ba6Gk7u-snQR0mAfWoFJxHvoMiz2TmBEXqzbQ_501PR8eoFHOFI7aPPBDwC4PP_ZfKD0X-C7tRn_3IsDH45tmFw_QUZw4zM13RmrAsoLHcVUDwohBBN_KF7bRTd-EGzQd-D/s320/%2528Amplifier%2529+Equation+24.jpg" style="cursor: pointer; display: block; height: 160px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></span></div>
<div>
<span class="Apple-style-span"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; font-size: 16px;"><br /></span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
<ol start="4" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l2 level1 lfo7;">Integrator</li>
</ol>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt; tab-stops: 0in; text-align: center;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598380943986425826" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyZ9g7dX3PqKheyQikStVWhLXz0wEYMWekK5Pz2f0sElxCQbm5rCasenYC-laDzI_SLVIkMY80M7NNhWNYRFVMwiefVxF6-8O7JUMPRi7YVWZqRnrznada-tV3TBHSK09Xvq25Y5uk5ln7/s320/%2528Amplifier%2529+Picture+12.jpg" style="cursor: pointer; display: block; height: 153px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></div>
<div class="Gambar" style="text-align: center;">
Picture 12: Integrator Amplifier</div>
<div class="SubSubBab" style="margin-left: 63.0pt; mso-list: none; tab-stops: .5in; text-indent: 0in;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt; text-align: justify;">
The basic of analizing this circuit is using the golden rule.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 1.25in; mso-list: l1 level1 lfo12; text-align: justify; text-indent: -27.0pt;">
III.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>V<sup>*</sup>= 0 or V<sub>+</sub>=V<sub>– </sub>, because of V<sub>+</sub> connect to the ground so: V<sub>+</sub>=V<sub>–</sub>= 0</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 1.25in; mso-list: l1 level1 lfo12; text-align: justify; text-indent: -27.0pt;">
IV.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span><i style="mso-bidi-font-style: normal;">i</i><sub>+</sub> = <i style="mso-bidi-font-style: normal;">i</i><sub>–</sub> = 0</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 1.25in; mso-list: l1 level1 lfo12; text-align: justify; text-indent: -27.0pt;">
<span class="Apple-style-span" style="line-height: normal;">From the kirchof, we can get:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598380283266782930" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2Gdg-i1yirbxmr_THz2P9FBjmT7LUfVn8oUi7-ZTsxL3Qx8Xn6iNM2swhxoxzc11pyLuZZEX4xpPInoxeuqFlTaNGGKOPFP-tNeXPKSgulNpwF7lktFwYF9XxjV-4KT2CCMFym7eV5xv0/s320/%2528Amplifier%2529+Equation+25.jpg" style="cursor: pointer; display: block; height: 24px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 63.0pt;">
Using the golden rule:</div>
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<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598379554525001010" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6VHuLa-6wHBrTAz0eWQtsLoJQJyfT3mPVj_R4IW7mzd403Gvh2rWyLhqafO9ElAl2aWU66fBqjKGShIzF-X8ckQ8dq8pD86KjFFPZricmzgvYgzwPlOCPf6yuT6lH5kl0D5IwLAD2Yg1l/s320/%2528Amplifier%2529+Equation+26.jpg" style="cursor: pointer; display: block; height: 184px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></div>
<div>
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><br /></span></div>
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<br /></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
<div class="SubSubBab" style="margin-left: 63.0pt; mso-list: none; tab-stops: .5in; text-indent: 0in;">
<o:p> </o:p></div>
<ol start="5" style="margin-top: 0in;" type="a">
<li class="MsoNormal" style="line-height: 150%; mso-list: l2 level1 lfo7; text-align: justify;">Penguat untuk instrumentasi <i style="mso-bidi-font-style: normal;">(Instrumentation amplifier)<o:p></o:p></i></li>
</ol>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: justify;">
An instrumentation amplifier is a differential op-amp circuit providing high input impedances with ease of gain adjustment through the variation of a single resistor</div>
<div align="center" class="MsoNormal" style="margin-left: 0.5in; text-align: center;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline;"><span class="Apple-style-span" style="line-height: 24px;"><br /></span><span class="Apple-style-span"><span class="Apple-style-span" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598375372647493426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp750OAgBf0FvvDBIJCSWiwTOR5r5dZCtuSr9JSvJnijBmWY-sMDJCfBmLCGqU0iiCKRq9o1wO8rfpSZNqM7MNMTJw6oG-0hH40GKieEe3qYpoUueupOw7rjYgbQU9RW87hk6m0nKlmaLa/s320/%2528Amplifier%2529+Picture+13.jpg" style="cursor: pointer; display: block; height: 320px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 258px;" /></span></span></span></div>
<div>
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><br /></span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-align: center;">
<i style="mso-bidi-font-style: normal;">Picture 13: Instrumentation Amplifier<o:p></o:p></i></div>
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<o:p> </o:p></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-align: justify;">
This intimidating circuit is constructed from a buffered differential amplifier stage with three new resistors linking the two buffer circuits together. Consider all resistors to be of equal value except for R<sub>G</sub> or R<sub>gain</sub>. The negative feedback of the upper-left op-amp causes the voltage at point 1 (top of Rgain) to be equal to V<sub>1</sub>. Likewise, the voltage at point 2 (bottom of Rgain) is held to a value equal to V<sub>2</sub>. This established a voltage drop across R<sub>gain</sub> equal to the voltage difference between V<sub>1</sub> and V<sub>2</sub>. That voltage drop causes a current through Rgain, and since the feedback loops of the two input op-amps draw no current, that same amount of current through Rgain must be going through the two "R" resistors above and below it. This produces a voltage drop between points 3 and 4 equal to:</div>
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</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6pt; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-align: -webkit-auto;">
<span class="Apple-style-span" style="line-height: normal;"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598378568871571490" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMjgea0q7pqp4GD2SYRRZQLnssol450bAyHhpIA_di2cqnf_Uh5r8MQtrQZ82zn0UWVfXnU0L5pnRVRa1WNaDAvi9sj1ukZBWwSbroLScy-gYFKG1Wyqt6uDo4J9MD7q13TkAeHe3iyodJ/s320/%2528Amplifier%2529+Equation+27.jpg" style="cursor: pointer; display: block; height: 48px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 320px;" /></span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6pt; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-align: left;">
<span class="Apple-style-span" style="line-height: normal;">The regular differential amplifier on the right-hand side of the circuit then takes this voltage drop between points 3 and 4, and amplifies it by a gain of 1 (assuming again that all "R" resistors are of equal value). Though this looks like a cumbersome way to build a differential amplifier, it has the distinct advantages of possessing extremely high input impedances on the V<sub>1</sub> and V<sub>2</sub> inputs (because they connect straight into the noninverting inputs of their respective op-amps), and adjustable gain that can be set by a single resistor. Manipulating the above formula a bit, we have a general expression for overall voltage gain in the instrumentation amplifier:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-align: justify;">
<span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; color: #0000ee; line-height: normal;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5598377917862714418" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEGVwT50M2TPhAUTx_WBT5any66OQ8Qv18q578YM8lN2sOmoZp3KbFXeP5bbwz7xK3StNr9g1iTrtUrqXZlhV3R0rc7qKq7gynyIdnymQjvSm9vK7goCft4x_EXsljFtqGnVnAAbPpJaTT/s320/%2528Amplifier%2529+Equation+27a.jpg" style="cursor: pointer; display: block; height: 85px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 181px;" /></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 6.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-align: justify;">
Though it may not be obvious by looking at the schematic, we can change the differential gain of the instrumentation amplifier simply by changing the value of one resistor: R<sub>gain</sub>. We could still change the overall gain by changing the values of some of the other resistors, but this would necessitate balanced resistor value changes for the circuit to remain symmetrical. Please note that the lowest gain possible with the above circuit is obtained with Rgain completely open (infinite resistance), and that gain value is 1.</div>
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(<a href="http://www.allaboutcircuits.com/vol_3/chpt_8/10.html">http://www.allaboutcircuits.com/vol_3/chpt_8/10.html</a>, 10<sup>th</sup> April 2011, 01:40 PM)</div>
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*Thanks*</div>
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</div>skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-78111916390477961502011-02-13T00:46:00.000-08:002012-05-16T22:40:39.466-07:00Industrial Management (TI4004)<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_2G0RjiKjj5dVof5fAsParvUioMFDJPulurfhtZ6T4IBnhcMJqFT2T9SjQaCpbNb5fpcV5wNJPAPbFoxGpF33VmEhSAJVkgJt_chokbRKPaRTGJ7_Cog3rOyyXcJEpK_MEjC4-ocyXm-7/s1600/P7078420.JPG"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5573378234253974946" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_2G0RjiKjj5dVof5fAsParvUioMFDJPulurfhtZ6T4IBnhcMJqFT2T9SjQaCpbNb5fpcV5wNJPAPbFoxGpF33VmEhSAJVkgJt_chokbRKPaRTGJ7_Cog3rOyyXcJEpK_MEjC4-ocyXm-7/s320/P7078420.JPG" style="cursor: hand; cursor: pointer; float: right; height: 240px; margin: 0 0 10px 10px; width: 320px;" /></a><br />
<br />
Management help you too get your <b>goal</b>. More than that, management make you can achieve the goal <b>effectively</b>. <br />
<div>
The earth is become small because of human greedy. Some greedy people use management not to lives effectively. They thing with management they can get unlimited live, unlimited financial, unlimited resource. The thruth is no such a things in this world are unlimited. </div>
<div>
The management helps people to deal with the limited of resource. Management helps people to live with other people with lovely.</div>
<div>
From the knowledge I get, I'd like to present the lecture note for all of you who want to learn the basic of management. Especially i present this for all brother & sister that took <b>TI 4004 class, the class of Industrial Management (for FTMD) , at Bandung Insititute of Technology</b>.</div>
<div>
<br /></div>
<div>
DOWNL0AD:</div>
<div>
<br /></div>
<div>
<a href="http://www.ziddu.com/download/13940511/TI4004-Catatankuliah1.pdf.html">Catatan Kuliah 1</a></div>
<div>
<a href="http://www.ziddu.com/download/13940518/TI4004-Catatankuliah2.pdf.html">Catatan Kuliah 2</a></div>
<div>
<a href="http://www.ziddu.com/download/14285968/TI4004-Catatankuliah3.pdf.html">Catatan Kuliah 3</a></div>
<div>
<a href="http://www.ziddu.com/download/14285969/TI4004-Catatankuliah4.pdf.html">Catatan Kuliah 4</a></div>
<div>
<a href="http://www.ziddu.com/download/14285966/TI4004-Catatankuliah5.pdf.html">Catatan Kuliah 5</a></div>
<div>
<a href="http://www.ziddu.com/download/14924792/TI4004-Catatankuliah6.pdf.html">Catatan Kuliah 6</a> (sudah ada bahannya tp belum selesai)</div>
<div>
<a href="http://www.ziddu.com/download/14285967/TI4004-Catatankuliah7.pdf.html">Catatan Kuliah 7</a></div>
<div>
Kuliah 8 (UTS)</div>
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<a href="http://www.ziddu.com/download/14924791/TI4004-Catatankuliah9dan10.pdf.html">Catatan kuliah 9 dan 10</a> (belum lengkap, mohon klo ada yang punya bahan nya, bisa di share, terutama soal2 latihan dan PR)</div>
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<a href="http://www.ziddu.com/download/14923220/TI4004-Catatankuliah11.pdf.html">Catatan Kuliah 11</a></div>
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<a href="http://www.ziddu.com/download/14923219/TI4004-Catatankuliah12.pdf.html">Catatan Kuliah 12</a></div>
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<a href="http://www.ziddu.com/download/14924793/TI4004-Catatankuliah13.pdf.html">Catatan Kuliah 13</a> (belum lengkap)</div>
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Kuliah 14 (UAS)</div>
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<br /></div>skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0tag:blogger.com,1999:blog-9034572127535224290.post-772425075573063792010-02-25T23:33:00.000-08:002014-07-22T09:17:13.379-07:00Keep DreamingKeep Dreaming . . . Sepintas itu adalah kata-kata yang pantas kita ucapkan untuk orang -orang yang biasanya bermalas-malasan. namun sebenarnya ada hal yang lebih menarik.<br />
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<em>Dreaming</em> adalah salah satu Anugrah terbaik yang Tuhan ciptakan bagi manusia. <em>Dreaming</em> bisa datang membawa pertanda buruk, tetapi dreaming juga terkadang telah membuka pandangan kita yang sempit. Bermimpi terkadang bisa membuat manusia lupa akan sang pencipta hingga rela menghalalkan segala cara untuk mencapainya. Tetapi mimpi juga yang membuat manusia bisa melihat "jalan Tuhan" untuk menghadirkan damai surga di dunia ini.<br />
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Tak bisa dibayangkan, seandainya manusia hidup tanpa ber"mimpi". Hidup tanpa mimpi bagaikan hidup tanpa harapan dan tujuan. Manusia menjadi tidak lebih dari seonggok daging yang akan segera kembali menjadi tanah. Tanpa mimpi tidak ada burung-burung besi yang kini membawa manusia melintasi pulau, selat, bahkan samudera tanpa terhalangi.<br />
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Kini, himpitan dan tekanan dunia membuat manusia semakin takut untuk bermimpi. Mimpi-mimpi pun semakin murah di obral dengan harga kecurangan demi ego pribadi semata. Mimpi seharusnya menjadi Anugrah yang bisa dirasakan siapa saja.<br />
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Oleh karena itu, jangan berhenti BERMIMPI. Mintalah pada Sang Khalik untuk menajamkan setiap pikiran kita agar mampu menembus awan gelap setebal dan setinggi apapun. Mintalah juga perhiasan-perhiasan Kejujuran, Cinta dan Damai pada-NYA, sehingga kita bisa menghiasi setiap mimpi itu dengan keindahan yang SEJATI.<br />
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Maju terus wahai Pejuang MIMPI . . . :)skysmithhttp://www.blogger.com/profile/05625113411834150130noreply@blogger.com0