Write a C++ program to implement the Example on Chapter 6 Lecture 1 Slide 5. You need to print a table like Table 6.2 and to find optimum step size from the table (minimum error).

2- Complete your program byimplementing the Example on Chapter 6 Lecture 1 Slide 8. And compare the result with optimum step size found on part 1 above.

Central-difference formula - Example Let f(x) = cos(x). Use central-difference formula of order 0(h) with step size h = 0.1, 0.01 , 0.001 , 0.0001 . To approximate f'(0.8) Note that the exact value of f'(0.8) = - sin(0.8) = -0.717356090899 If h = 0.01 f'(0.8) f(0.81)-f(0.79) 2x0.01 = -0.717344150 Table 6.2 Numerical Differentiation Using Formu Step Approximation by Error using size formula (3) formula (3) 0.1 -0.716161095 -0.001194996 0.01 -0.717344150 -0.000011941 0.001 -0.717356000 -0.000000091 0.0001 -0.717360000 -0.000003909 Numerical Analysis - prepared by: Eng Shatha Al-Hasan Optimum step-size - Example Let f(x) = cos(x) and = 0.5 x 10-9 Find optimum step size for Central-difference formula of order 0 (h?) |f(3)(x) = |sin(x)] = 1 M=1 .h= (3x0.5X10-9 = con = 0.001144714 Note that from previous example, optimum step size h = 0.001 Numerical Analysis - prepared by Eng Shatha Al-Hasan