# Math Help - advanced calc diffrential prob

1. ## advanced calc diffrential prob

let g(x) be such that l g(x) l <= M for all x in [-1,1]
let h(x) = (x^2)g(x) if x is not equal to 0
= 0 if x is equal to 0
show that h(x) is diffrentiable at x = 0 and find h'(0)

2. $0 \leq \vert \frac{h(x)}{x} \vert = \vert xg(x) \vert \leq M\vert x \vert$ so taking $x\rightarrow 0$ we have $h'(0)=0$

3. can u break down a little more please

4. Remember that $h'(0)= \lim_{x\rightarrow 0} \frac{h(x)-h(0)}{x-0} =\lim_{x\rightarrow 0} \frac{h(x)}{x}$ and to evaluate the limit we use the squeeze theorem.

5. thanks so much