# Proof of a limit involving definition of differentiability

1. Apr 2, 2012

### mrchris

1. The problem statement, all variables and given/known data
let the function f:ℝ→ℝ be differentiable at x=0. Prove that lim x→0
[f(x2)-f(0)]
______________ =0
x

2. Relevant equations

3. The attempt at a solution
I am kind of lost on this one, I have tried manipulating the definition of a differentiable function at x=0 and I am not making much progress. I am not just looking for an answer here, this actually a review problem for a test and I am really trying to understand it so any help would be appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 2, 2012

### Curious3141

Try L' Hopital's Rule.

3. Apr 2, 2012

### mrchris

I am in an analysis class and we have not yet proved L' Hopital's Rule so I can not use it in this proof.

4. Apr 2, 2012

### Dick

Use the change of variable u=x^2. Now think about the limit as u->0.