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## Homework Statement

Prove that if f''(x) exists and is continuous in some neighborhood of a, than we can write

[tex]

f''(a)= \lim_{\substack{h\rightarrow 0}}\frac{f(a+h)- 2f(a)+f(a-h)}{h^2}

[/tex]

## The Attempt at a Solution

I just proved in the first part of the question, not posted, that

[tex]

f'(x)= \lim_{\substack{h\rightarrow 0}}\frac{f(x+h)- f(x-h)}{2h}

[/tex]

but I am not sure how to use it for the 2nd derivative, since there is no "formula" in my book to get started with for the second derivative limit, but only for the first derivative.

Thank you in advance