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## Homework Statement

if

*f*' is continuous, show that:

[tex]\mathop{\lim}\limits_{x \to 0}(\frac{f(x+h)-f(x-h)}{2h})=f'(x)[/tex]

be sure to explain why

*f*' must be continuous

## Homework Equations

not really any equations, this is for AP Calc BC and we've just done L'Hospital's theorem and the derivatives/integrals of logs and inverse trig functions.

## The Attempt at a Solution

I know that as x-->0 it becomes [tex]\frac{f(h)-f(-h)}{2h}[/tex] . I thought about proving that the difference quotient can be manipulated into the above formula, but haven't had any success.

Any pointers?