Question

1) This problem studies the errors due to the approximation of the first derivative of a given function f(x) using the forward and centered difference methods. For this problem, we consider f(x)=sin(x). a) First, we will investigate the effect of the step size h on the first derivative approximation. Set h=10', with i =[-20:0.5:0) and x=1-0.1. Write Matlab code that evaluates the total errors with respect to the analytic derivative at the given x value above of both the forward and centered difference estimates of S'(x), for each of the step size h values. Compile the following results on a 3-panel vertical plot with log-log scaling on the axes and the error terms absolute-valued: i) Panel 1, two plots: the (absolute value of the) total error of the forward difference scheme versus step size h and the (absolute value of the) most significant truncation error term for the first forward difference method, i.e., 2!

please show me a Matlab script that will compute the total errors of the approximation due to the given function, also include the panel plot as well, thank you.