Consider the function f (x) = x − cos x.
(a) Use a graphing utility to graph the function and verify that there exists a zero between 0 and 1. Use the graph to approximate the zero.
(b) Starting with x0 = 1, generate a sequence x1, x2, x3 , . . . , where xn = cos(xn−1). For example, x0=1, x1=cos(x0), x2=cos(x1), x3=cos(x2), . . . . What value does the sequence approach?