We want to explore the ability of Newtons method to find roots to the equation sin(x) =

We want to explore the ability of Newton’s method to find roots to the equation sin(πx) = 0. You should already know the roots of this equation. Write a MATLAB program that determines the roots of the equation for initial guesses x = 0, 0.01, 0.02, . . . , 1.99, 2.00 by using Newton’s method. Your program should generate a plot of the root produced by Newton’s method as a function of the initial guess. You should explain your plot in the context of what you should know about convergence of Newton’s method.