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F. There are fun examples for which Newton's method produces interesting sequences of iterates. Experiment with some of the following. Pick one (or two) and discuss the behavior of the method. You may wish to include graphical illustration of what you observe in addition to a table of interations. i. The true root of f(3) = 3r is clearly a = 0. Newton's method can not be used to find this root for any choice of 10 =0. TH Hot ii. The equation r" – 50 = 0 has three solutions 0, v5 and - v5. Consider Newton's method with To = 1 or 10 = -1. . iii. f(1) = 13 2.1 + 2 has one real root close to -2. What happens with an initial gues To = 0? If an initial guess in the interval -0.1 < r < 0.1 is chosen, after several iterations, some interesting behavior is seen. What is perhaps more surprising is what happens if a really bad guesse.g. Io = 5—is taken.