1. Consider solving the nonlinear equation f(x) = +1 -2 = 0. Let $(1) = 1 + f(x). The function (2) has two fixed points r* = 1 and r* = -2. (a) Write a computer program to check whether the iteration, In+1 = 4(x) for n = 0,1,2,..., generates a convergent sequence with different initial guess to #1, -2, 0, -1. (b) Write a computer program to check the convergence of the iteration above accelerated by Aitken's technique, which now reads yo y2 - v yo + y2 - 21 with yo = {m, Y1 = 4(90) and y2 = 4(91), for n = 0,1,2,..., until the absolute value of the nonlinear function is sufficiently small, f(*n+1)