} (2-4) 1. (straction of Cube Roots). )(a) Let A be a real number. Show that 1 NA 2 (3.1) 3 thereby reducing the problem of extracting of the cube root of A to a fixed point problem (b) Assume further that A > I, and then show that the corresponding iteration function ()(2x + satisfies the conditions of the main statement on convergence of the FPI from the lecture notes on the closed interval (VA. Al that I show that VA(0) CA for all ETVA, A) and that there is a constant ke (0.1) satisfying () for all EVAA) (1) Based on your result in (I), apply the FPI for the function 9(a) to find an approximation py of the cube root of 21.64 by taking po - 21.64 as the initial approximation and using the second stopping criterion with the tolerance - 10-4 All calculations are to be carried out in the PPA. Present the results of your calculations in a standard output table of the form рані Pa REP-1) (Your answers to the problem should therefore consist of a complete solution to purt (i) and a table you have to create in part (ii), followed by a Conclusion regarding the required approximation Pn.)
