Math 181 Miniproject 3: Texting Lesson.md
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My lesson Topic
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<style>
body {
background-color: #eeeeee;
}

h1 {
color: green;
margin-left: 40px;
}

.gray {
margin-left: 50px ;
margin-right: 29%;
font-weight: 500;
color: indigo;
background-color: #cccccc;
border-color: #aaaaaa;
}

.blue {
display: inline-block;
margin-left: 29% ;
margin-right: 0%;
width: -webkit-calc(70% - 50px);
width: -moz-calc(70% - 50px);
width: calc(70% - 50px);
font-weight: 500;
color: yellow;
border-color: #336699;
background-color: #337799;
}

.left {
content:url("https://i.imgur.com/rUsxo7j.png");
width:50px;
border-radius: 50%;
float:left;
}
.right{
content:url("https://i.imgur.com/5ALcyl3.png"); width:50px;
border-radius: 50%;
display: inline-block;
vertical-align:top;
}
</style>

<div id="container" style=" padding: 6px;
color: #fff;
border-color: #336699;
background-color: #337799;
display: flex;
justify-content: space-between;
margin-bottom:3px;">
<div>
<i class="fa fa-envelope fa-2x"></i>
</div>
<div>
<i class="fa fa-camera fa-2x"></i>
</div>

<div>
<i class="fa fa-comments fa-2x"></i>
</div>
<div>
<i class="fa fa-address-card fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-phone fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-list-ul fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-user-plus fa-2x" aria-hidden="true"></i>
</div>
</div>

<div><img class="left"/><div class="alert gray">
Hey on the exam I got number 2 wrong 😭.Did you get it right if so can you help me? Its the question using the limit definition of derivative.

</div></div>

<div><div class="alert blue">
Yeah!😅 I can help you so for part a.) all what was being asked is what is the limit definition of the derivative f'(x) of a function f(x). Basically the question was asking dor the formula.Do you rememeber what it is?

</div><img class="right"/></div>

<div><img class="left"/><div class="alert gray">
I think I remember.
</div></div>

<div><img class="left"/><div class="alert gray">

is it $lim_{h→0}\
\frac{f\left(x-h\right)+f\left(x\right)}{h}$ ?

</div></div>

<div><div class="alert blue">

No not quite you have you signs mixed up the limit defination of the derivative is $lim_{h→0}\
\frac{f\left(x+h\right)-f\left(x\right)}{h}$. Here lets try an example: $f(x)=x^2-2x$

</div><img class="right"/></div>

<div><img class="left"/><div class="alert gray">

Oh okay so for part b.) do we plug in the function $x^2-2x$ into $lim_{h→0}\
\frac{f\left(x+h\right)-f\left(x\right)}{h}$

</div></div>
<div><img class="left"/><div class="alert gray">

Like this $lim_{h→0}\
\frac{f\left(x^2-2x+h\right)-f\left(x^2-2x\right)}{h}$ ?😕

</div></div>
<div><div class="alert blue">
No you want to plug in (x+h) in to the function.Let me show you how to do the problem:


</div><img class="right"/></div>

<div><div class="alert blue">

Here's how to do a problem like number 2 on the exam.This looks like a lot,but I organized it in color and steps to make it easier for you.

</div><img class="right"/></div>
<div><img class="left"/><div class="alert gray">

Omg‼️ Thank you this is helpful let me try to do one on my own.😅

</div></div>
<div><div class="alert blue">
No problem just text me if you have any questions .

</div><img class="right"/></div>

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