if f is differentiable in $\displaystyle f(x_{0})$ so: $\displaystyle lim_{h\rightarrow0}\frac{f(x_{0}+h)-f(x_{0}-h)}{2h}=f'(x_{0}) $
i need to know if this is right or false... i tried to use arithmetic rules on this but i got nothing..
if f is differentiable in $\displaystyle f(x_{0})$ so: $\displaystyle lim_{h\rightarrow0}\frac{f(x_{0}+h)-f(x_{0}-h)}{2h}=f'(x_{0}) $
i need to know if this is right or false... i tried to use arithmetic rules on this but i got nothing..
If f is differentiable, then the given limit exists and is what you say it is, so you are correct. The converse is not true, though. The limit can exist for functions that are not differentiable - take $\displaystyle f(x)=\frac{1}{x^2}$ and $\displaystyle x_0=0$, for example.
- Hollywood