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. chapter 6 slide 5 Central-difference formula - Example 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 Table 6.2 Numerical Differentiation Using Formu f'(0.8) = f(0.81)-f(0.79) 2x0.01 Step size 0.1 0.01 0.001 0.0001 Approximation by formula (3) -0.716161095 -0.717344150 -0.717356000 -0.717360000 Error using formula (3) -0.001194996 -0.00001194! -0.000000091 -0.000003909 = -0.717344150 [1] 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) chapter 6slide 8 [f(3)(x) = |sin(x)] = 1 M = 1 3x0.5X10-9 h = = = 0.001144714 1 . Note that from previous example, optimum step size h = 0.001