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Problem 2. (25%) For given x0), say, x(0) = 1.0, compute the sequence x(1), x(2), x(3), ..., x(N), up to a suitably large value of N, e.g., N = 20, or higher where necessary, using the recurrence relation 2(k+1) = f(x(k)), k = 0, 1, 2, 3, ..., where f(x) = 290.+5 . Describe in a few words the observed behavior of the sequence. In particular, does the sequence approach a limiting value? If yes, then do you recognize what this limiting value is? Does the limiting value depend on x(0) ? Also compute the sequence with f(x) = cx(1-x), for five cases, namely, c = 0.95, c= 1.55, c= 2.0, c = 3.6, and c = 3.98. For each of these cases choose the value of x(0) to lie between 0 and 1, for example, x(0) = 0.1. In each case describe the observed behavior of the sequence