# Math Help - Homework

1. ## Homework

Use l' Hopital's Rule to find the limit. Show your work.

Lim cosx-1/2x^2 is 0/0 form
x->0

2. Originally Posted by Emmeyh15@hotmail.com
Use l' Hopital's Rule to find the limit. Show your work.

Lim cosx-1/2x^2 is 0/0 form
x->0

$\lim_{x\to0}\frac{\cos\!\left(x\right)-1}{2x^2}$

Is this what you mean?

3. Yes sorry i didnt know how to make that arrow!!!

4. Originally Posted by Emmeyh15@hotmail.com
Yes sorry i didnt know how to make that arrow!!!
In applying L'Hopitals rule, you need to differentiate both numerator and denominator of the limit. Thus we see that

$\lim_{x\to0}\frac{\cos\!\left(x\right)-1}{2x^2}=\lim_{x\to0}\frac{-\sin\!\left(x\right)}{4x}$

Again, this limit has the indeterminate form $\frac{0}{0}$

So, I leave it for you to apply the rule one more time.

Does this make sense?