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1. (fraction of Cube Roots). a) Let A be a real number. Show that 1 28+ thereby reducing the problem of extracting of the cube root of A to a fixed-point problem. (b) Assume further that A > I, and the show that the corresponding iteration function 1) satisfies the conditions of the main statement on convergence of the FPI from the lecture notes on the closed interval A4, that show that VĀ <$() CA for all 1 EVA, A} and that there is a constant k € (0.1) atlying (+) for all E (VAA) (1) Based on your result in (l), apply the PPI for the function to find an appreciation of the cube root of 9.62 by taking Po 9.624 the initial approximation and the second stopping criterion with the tolerance - 10-! All contos are to be carried out in the FPA Present the mult of your calendations in a standard output table of the form PREPAN! Your anreth the problem so therefore cont of a complete solution to andatite you love to rate in partea conclusion trading the required approximation PN)