Post #2

So it's finally the end of week number two of school, and of Calculus. I won't even joke with you guys, I've been completely lost at some point during this week. I think I'm pretty set on all the different derivatives now. The most important thing that I continue to screw up though, however, is when there is a lot of canceling out to do. I tend to be lazy and try to find shortcuts in skipping steps but it ends up biting me in the behind anyway. :-(

So, things that completely confused me until Thursday...

When you take the derivative of uⁿ it is nu^n-1. Well, I didn't realize that say you have...
(x²-1)² you actually have to use the formula nx^n-1 times u'. So you get 2(x²-1)(2x) so ultimately we get 4x(x²-1).
Hope everyone remembers to do this...

After realizing that every single derivative so far that we've had is times by u' I don't think this will be hard to remember.

Anyway, I think that the test on Wednesday will be really hard...I know it covers limits so I figured I'd help everyone out.

When you take the limit as x goes to infinity, the rules are as follows
1) If the degree of the top is larger than the degree of the bottom, its infinity.
2) If the degree of the top is equal to the degree of the bottom, it is the leading coefficient of the bottom divided by the leading coefficient of the bottom.
3) If the degree of the top is smaller than the degree of the bottom, it is 0.

Other things include vertical asymptotes. To do this, you set the bottom part of the fraction equal to 0. Asymptotes occur at these x-values.

Horizontal Asymptotes follow the rules of limits. (the 1-3 of above). The asymptotes will either not occur (rule 1), at y=coeffi/coeffi (rule 2) or at y=0 (rule 3).

I won't explain them here but don't forget to study removeables, jumps, and infinite discontinuities :-p.