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). 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 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 -0.00001194 0.001 -0.717356000 -0.000000091 0.0001 -0.717360000 -0.000003909