Math 181 Miniproject 3: Texting Lesson.md
---
My lesson Topic
===

<style>
body {
background-color: #eeeeee;
}

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

.gray {
margin-left: 50px ;
margin-right: 29%;
font-weight: 500;
color: #000000;
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: #fff;
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, is this Emily from Math 181?

</div></div>

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

Yeah, who's this?

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

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

This is Casey, I'm the one who asked for your number after class.

</div></div>

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

Could you help me with problem 3?

</div></div>

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

Yeah of course, the one about findin the limit and a tangent line?

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

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

Yeah, I get that the equation line will be all over h, but I don't know what goes on too in the numerator

</div></div>

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

Okay, so it's great that you know in the limit definiton f(x)= lim as h approaches 0 that the divisor is h. The numerator would be f(x+h)-(f(x). This seems tricky but its not. I know you know f(x) becaue its given in the problem that f(x)=3x^2-5x+10. To getf(x+h), we fill in an x+h instead of just x so its [3(x+h)^2-5(x+h)+10] and then of course minus f(x) which we said was 3x^2-5x+10. Dont forget to distrubute the negative sign.After you simplify you should get 6x-5. Its implifies to 6x+3h+5, but since h is 0 we dont need it.
(http://sergeballif.github.io/NSC-Math-181/Specifications.html).

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

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

I ended up simplifying and I got 6h-5. We use this to find the tangent line right? When x=5? Do we just fill in 5 for x. I forgot the formula.

</div></div>

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

So we actually use a diferent forumla first but we plug in five there. ITs the formula y=f(5)+f'(5)(x-5). Ill show you my work
=[3(5^2-5(5)+10)]+[6(5)-5](x-5)
=75-25+10(x-5)
=60+25(x-5)
Hope this helped!!

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

---

To submit this assignment click on the Publish button . Then copy the url of the final document and submit it in Canvas.