Please write c++ program to explain each question! Thanks in advance!

That was the original problem, and I didn't delete any of the mathematical premises. This question is derived from the "Round Off Error" part of Numerical Analysis.

3. a. (i) Compare the accuracy of the following three formulas for approxi- mating the derivative, f'(x): Mi(n) = f(x + h) f(x) h ) Mach)-f(x+h)-f( x 2h Mach) -f(x + 2h) + 4f (x + h) - 3f (x) 2h In particular, test the above approximations when f(x) = x/3, x = 0 or r = 1, and h = 10-P, p = 3, 4, 5,..., 20. (ii) As h is decreased, the error becomes smaller, until a critical value of h is reached, after which point the error starts to increase as h decreases. Find the critical h, herit, experimentally. Note: in order to avoid problems in evaluating x*/when x