Q:

find the limit of (f(x) - f(-x)) /x when x goes to zero

Please some one help me to do the following problem.
If $f : \mathbb R\to\mathbb R$ is differentiable at $0$ and $f'(0) =1$, find $\lim\limits_{x\to 0} \frac{f(x) - f(-x)}x$.

A:

$\displaystyle \lim_{x \to 0} \frac{f(x) - f(0)}{x} = f'(0)$
$\displaystyle \lim_{x \to 0} \frac{f(-x) - f(0)}{-x}=$$\displaystyle \lim_{y \to 0}\frac{f(y) - f(0)}{y}=f^{'}(0)$

