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Difference Quotients, Formulas and Rate of Convergence

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1. (Finite Differences) Let f(x) = cos(x+2). Compute f'(0) using the difference quotients given below and step-size h = 2^-n, n = 1,... .5.
D + f = (f(x + h) - f(x))/h
D o f= (f(x+h)_f(xh))/2h
For each difference formula, make a table with the following information.
column 1: h
column 2: Df
column 3: f'(0) ? Df
column 4: (f'(0) ? Df)/h
column 5: (f'(0) ? Df)/h2
column 6: (f'(0) ? Df)/h3

Discuss the results, especially the rate of convergence.

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