$\displaystyle f $ is a differentiable function at $\displaystyle x=1$.prove that if $\displaystyle \lim_{h\rightarrow0}\frac{f(1+h)}{h}=1 $

so, $\displaystyle f(1)=0 $ & $\displaystyle f'(1)=1 $

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- Apr 20th 2013, 09:16 AMorirDifferentiable function problem
$\displaystyle f $ is a differentiable function at $\displaystyle x=1$.prove that if $\displaystyle \lim_{h\rightarrow0}\frac{f(1+h)}{h}=1 $

so, $\displaystyle f(1)=0 $ & $\displaystyle f'(1)=1 $ - Apr 20th 2013, 09:26 AMPlatoRe: Differentiable function problem
- Apr 20th 2013, 09:49 AMorirRe: Differentiable function problem
i actually don't know what to answear to that.. :S

- Apr 20th 2013, 09:53 AMPlatoRe: Differentiable function problem
- Apr 20th 2013, 11:03 AMorirRe: Differentiable function problem
this lim doesn't exist... so? how this helps me?

- Apr 20th 2013, 11:12 AMPlatoRe: Differentiable function problem
You are given that both

$\displaystyle {\lim _{h \to 0}}\frac{{f(1 + h)}}{h}\quad \& \quad {\lim _{h \to 0}}\frac{{f(1 + h) - f(1)}}{h}$**EXIST**.

Now doesn't that imply that $\displaystyle {\lim _{h \to 0}}\frac{{f(1)}}{h}$ must also exists?

If so, what does that tell you about $\displaystyle f(1)~?$ And why? - Apr 20th 2013, 11:40 AMorirRe: Differentiable function problem
i guess it tells me that $\displaystyle f(1)=0 $...

- Apr 20th 2013, 11:44 AMPlatoRe: Differentiable function problem
- Apr 20th 2013, 11:51 AMorirRe: Differentiable function problem
1! thank you...