can someone please help me with this

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)

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- Nov 21st 2009, 09:45 PMrphagooadvanced calc diffrential prob
can someone please help me with this

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) - Nov 21st 2009, 09:52 PMJose27
$\displaystyle 0 \leq \vert \frac{h(x)}{x} \vert = \vert xg(x) \vert \leq M\vert x \vert$ so taking $\displaystyle x\rightarrow 0$ we have $\displaystyle h'(0)=0$

- Nov 21st 2009, 10:02 PMrphagoo
can u break down a little more please

- Nov 21st 2009, 10:17 PMJose27
Remember that $\displaystyle h'(0)= \lim_{x\rightarrow 0} \frac{h(x)-h(0)}{x-0} =\lim_{x\rightarrow 0} \frac{h(x)}{x}$ and to evaluate the limit we use the squeeze theorem.

- Nov 21st 2009, 10:27 PMrphagoo
thanks so much