CPE 200 (Numerical Analysis) Assignment #4 - CLO 4 Due: Saturday 9/1/2021, 23:55 1- 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 by implementing 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 Ch6 lec1 slide 5 Let f(x) = cos(x). Use central-difference formula of order 0(ha) 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 (1) Optimum step-size - Example Ch6 lec1 slide 8 Let f(x) = cos(x) and = 0.5 x 10-? Find optimum step size for Central-difference formula of order 0(ha) |f(3)(x)] s (sin(x)= 1 = M = 1 (3x0,5x10 = 0.001144714 Note that from previous example, optimum step size h = 0.001