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Using the Taylor formula for f(x+h) and f(x-h) with f ''' in the error term, find the error of the approximate formula f '' (x) = (f(x+h)+f(x-h)-2f(x))/(h^2) in terms of f ''' (eta), for some point eta between x-h and x+h. Then give an upper bound for the absolute error assuming that |f ''' (t)| =< M for t between x-h and x+h.
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