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.
Please see the attached file for the fully formatted problems.
Difference Quotients, Formulas and Rate of Convergence are investigated. The solution is detailed and well presented.