Calculus Homework #1

So our first homework assignment is a bunch of problems that (in my opinion) help us remember all the math we’ve learned up to this point, in order to jog our memories before we delve into the depths of calculus. Sadly, it’s been quite some time since I’ve been in a math class. I graduated High School in 2004, and have only taken math once since then. I didn’t intend on ever taking it again, until about a week ago when I decided to switch to a biology major (so I can get into med school *fingers crossed*)…

Luckily I have some awesomely smart Facebook friends who referred me to the following website for help: Khan Academy. They also told me about an iPhone app (it’s free!) called TeXIT, which is kind of like latex but useful if you’re doing a blog post from your iPhone… just in case any of you didn’t know, you can do WordPress posts from the WordPress App. I also found a useful site for latex coding.

While working on my homework I found a second helpful website that helped me figure out the answer to factoring a difficult cube factoring problem. In case any of you wanted to know a good formula for this:

$x^3+27$ can be factored by using the following formula $a^3+b^3=(a+b)(a^2-ab+b^2)$

I won’t give away the answer, but it helped a LOT. Here’s the website if you want to learn more. I found that I have forgotten many of the algebraic formulas so this website may just save my life.

OK so it’s confession time. I pride myself in being quite knowledgeable with Algebra. I taught myself Algebra in homeschool in 5th and 6th grade, and I absolutely LOVE it. I know, I’m sick like that. But my weaknesses in math show up when the graphs come out. I can’t explain it. I have this mental block when it comes to graphing. You can give me slope and for the life of me I can’t remember $\dfrac {rise}{run}$ .

For example: I got to the problem “Find the equation of the line (in slope-intercept form) of the line that passes through (-8,8) and (4,5). Suddenly my mind went blank… it looked kind of like this:

Maybe it's not calculus I'm afraid of but the little death symbols all over my paper...

So I decided that another good idea would be to make a list of the equation forms I need to know.

Slope-Intercept: $y=mx+b$

Slope: $m=\dfrac{y_2-y_1}{x_2-x_1}$

point-slope form: $y-y_1=m(x-x_1)$

m= slope of the line

b= y-intercept

using this information I realize that my teacher would like me to solve this problem and lay it out in $y=mx+b$ form. Easy enough, right? So here’s how I solved it.

First I decided to solve for M. $m=\dfrac{5-8}{4-(-)8}$ which becomes $m=\frac{-3}{12}$ simplified $m=\frac{-1}{4}$ which means $m=\dfrac{-1}{4}$

Now I’m able to plug that in to the slope-intercept formula. $y=mx+b$ so $y=\dfrac{-1}{4}x-y$ becomes $b=y+\dfrac{-1}{4}x$ plug in either of the two points given and you get $b=\frac{-1}{4}*4+5$ then $b=1+5$ and $b=6$

Now you can create your slope-intercept equation $y=\dfrac{-1}{4}x+6$

TADA! I will get this slope stuff down!

There were many more problems I had to work on but for now that’s all I’m going to go over. Hopefully these helped any of you out there who might not remember slope or how to factor with cubed numbers.

Another issue I came across was when it came time to solve some of the quadratic equations that I could not factor. I had to use the actual quadratic equation formula, which I had forgotten. Here it is:

$Ax+Bx+C=0$ and how to solve for it without factoring $x= \dfrac{-B+-\sqrt{B^2-4AC}}{2A}$