# Homework Help: Weird Limit Problem

1. Sep 16, 2007

### Frillth

1. The problem statement, all variables and given/known data

Find the limit as x approaches 0 of x^2/(1-cosx).

2. Relevant equations

None.

3. The attempt at a solution

I know from L'Hopital's rule that the limit is 2, but I'm not supposed to use L'Hopital's rule to calculate it. What else can I do here?

2. Sep 16, 2007

### morphism

How about the identity cos(x) = 1 - 2sin^2(x/2)?

3. Sep 16, 2007

### Dick

You could also consider the power series expansion of cos(x) around zero.

4. Sep 17, 2007

### HallsofIvy

Multiply both numerator and denominator by 1+ cos(x). Then use the fact that
$$lim_{x\rightarrow 0}\frac{x}{sin(x)}= 1$$.