Compute the first 20 points of the orbits under N(x) for

Chapter , Problem 2

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Compute the first 20 points of the orbits under N(x) for the initial seeds x0 = 0, 0.05, 0.10, 0.15, 0.20,..., 0.90, 0.95, 1. Sketch the segment 0 x0 1. For each choice of x0, if the 20th point x20 in its orbit under N is within 0.01 of 0, color the point red; if x20 is within 0.01 of 1, color it blue; if x20 is within 0.01 of 2, color it green; and if none of these conditions holds, color it black. Is this figure consistent with your conclusions from Part 1? What implications does this picture have concerning the choice of the seed x0 for Newtons method?

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