Let f (x) have the second derivative at x = X. it is proved that the limit of [f (X. + H) - 2F (X.) + F (X. - H)] / h ^ 2 at h → 0 is equal to the second derivative of F (X.)
The process is as follows:
={[f(x+h)-f(x)]/h-[f(x)-f(x-h)]/h}/h
=[f'(x)-f'(x-h)]/h
=f''(x-h)
=f''(x),h->0
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