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Fundamental differential equation analysis

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If I be an open interval containing the point x. (x0) and suppose that the function f:I->R has two derivatives. Prove that

lim as h->0 (f(x.+h) - 2f(x.) + f(x.-h))/ h^2 = f"(x.)

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Solution Summary

The expert provides a proof using forward difference.

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By forward difference
f"(x.)= (f'(x+h)-f'(x))/h ...

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