Today I finally got my Calculus book. Yes, it’s the one with the eagle on it… a majestic bird, but I’m not sure why it’s on a calculus book.Like a Boss

I also did the homework on Math XL today and found the website to be VERY helpful for me in solving the math problems. You never realize how much you have FORGOTTEN about math until you need all that basic knowledge to move on to higher knowledge. I’m irritated I have neglected math for so long… because deep down inside I find myself liking it (a lot). Math will never lie to you… not if you put the right numbers in and use the right equation. I like that about math. See, there are a lot of unknowns in this world, mysteries of life… I even read this fascinating article about 6 scientific discoveries that defy the laws of physics. It’s a fun article. But math.. you solve a problem and it’s SOLVED. You can rest easy at night and maybe even get the recommended full 8 hours of sleep (what’s that like? I can’t remember…).

Anyway – on to Limits and Continuity. Limits are pretty sweet. It’s defining the height of a graph at a particular point on the graph. The limit from the left enters the point at a certain height, and then enters from the right at the same or different point. Easy. Then it gets a little more complicated. Does the line enter the point from the same height on both sides? If so… it’s probably continuous, but not necessarily.

Continuity is also a relatively simple concept. Easiest way to define whether something is continuous is whether or not you can draw the line without picking up your pencil. If you have to pick up your pencil, it’s not continuous. So if the line passes through the point in question (x), and continues on… it is continuous. Easy.

But then you have to complicate it for me. How do we determine the limits without looking at the graph with an equation? What if we change the equation from a polynomial to an exponential function? What is a polynomial function? What’s an exponential function? HOW DID I FORGET ALL OF THIS???

It’s true… that’s where I was about 8 hours ago… but luckily I have a brain and was able to look it all up and thought I would share the little nuggets of information with you guys in case you had a massive brain fart like I did.

1st thing I kinda forgot. A function f(x) = y. So when you solve for x, you get y. Capiche? Also.. if a vertical line (notice I did not say horizontal here) intersects a graph in more than one point, the graph is not the graph of a function.

I also forgot the differences between types of functions so I listed them out here:

1. Linear Function: y = f(x) = mx + b

2. A Quadratic Function: f(x) = ax^2 + bx + c where a, c, and c are real numbers and a\neq0.

3. Polynomial Function: f(x)= a_nx^n + a_{n-1}x^{n-1}+...+a_1x +a_0 where a_n, a_{n-1},...,a_1, and a_0 are real numbers called coefficients, with a_n\neq0.

4. Rational Function: f(x) = \dfrac{p(x)}{q(x)} where p(x) and q(x) are polynomial functions and q(x) \neq0

5. Exponential Function: f(x) = a^x where a>0 and a\neq1

These can all be found in Chapters 1 and 2 of our Calculus Book, but I find it useful to have these handy for solving problems, and I find things slowly coming back to me. I guess you have to force yourself into this full force or you won’t survive… at least me. I wish I were a genius with an amazing memory and a sponge-like brain, but I’m just not.