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. Write a C++ program to implement the Example on Chapter 6 Lecture 1 Slide 8. And compare the result with optimum step size found on part 1 above.

Chapter 6 Lecture 1 Slide 5.

Chapter 6 Lecture 1 Slide 8

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 Table 6.2 If h = 0.01 Numerical Differentiation Using Formu Step size f'(0.8) = f(0.81)-f(0.79) 2x0.01 Approximation by formula (3) -0.716161095 -0.717344150 -0.717356000 -0.717360000 0.1 0.01 0.001 0.0001 Error using formula (3) -0.001194996 -0.000011941 -0.000000091 -0.000003909 = -0.717344150 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(ha) \f(3)(x) = sin(x)= 1 M = 1 (3x0.5x100 .hr = = 0.001144714 M 1 . Note that from previous example, optimum step size h = 0.001