Third Post

So this week in Calculus seemed even easier than the rest. It's funny because when I was writing my last two posts I had exactly on my mind what I wanted to write because I knew what was frustrating me or what wasn't. This week--that isn't the case. So, what did we do?

We reviewed derivatives more and more. We had a test on them Wednesday so all Monday and Tuesday we made SURE we knew those things back to back. We got plenty of worksheets to make sure that we had a good grasp on them--and I do have a good grasp.

Next thing was that we needed to study other things than derivatives for the test. We had to study discontinuity. We studied removeables, jumps, and vertical and horizontal asymptotes. For removeables, it's pretty easily done to identify. All you do is factor the top and factor the bottom completely. Then if any of the factors match, you know there is a removeable there. For vertical asymptotes, anything left on the bottom is where the asymptote is. For horizontal asymptote, there are 3 rules:
1. If the degree of the top is bigger than the degree on the bottom, there is no limit
2. If the degree on the top is the same as the degree on the bottom, you divide the coefficients
3. If the degree on the top is smaller than the degree on the bottom, then the answer is 0.

So using all of this, we have this for example (after factoring the top and bottom)

(x+3)(x+4)
------------
x(x+1)(x+3)

So we know that there is a removeable at x=-3.
There are vertical asymptotes at x=0 and x=-1.
There is a horizontal asymptote at y=0 because the degree of the top is 2 which is less than 3.

Thursday we started to learn new things like concavity, the graphs of derivatives and other things...but I'm not sure if I grasps all of that completely because I wasn't there friday to go over it again. :-\

Hopefully maybe someone can go over it all with me and the applications of it. Please. :-)


-John