Can someone give me a quick lesson on solving for the limits of trig functions. my teacher didn't do a very good job of it, and she expects us to take a quiz after the first day. i'm in so much trouble, so if someone could help
This is a bit too vague I think. There's quite a lot of material I can think of that has to do with trig limits.
Here's a link that covers two important special limits, with some examples:
Special Trigonometric Limits - Library of Math
If you ask some specific questions, I can help you more.
#1)$\displaystyle \lim_{x \rightarrow 0} \frac{x^2}{1-\cos^2(x)}$. (1)
Use $\displaystyle \sin^2(x)+\cos^(x)=1$.
(1) = $\displaystyle \frac{x^2}{\sin^2(x)}= \left( \frac{x}{\sin(x)} \right) ^2= \left( \frac{\sin(x)}{x} \right) ^{-2}$
See where this is going?