Question: (a) Apply Newton's iterative method to the polynomial f (x) D x n a, where n is a positive integer, to show that if x1

(a) Apply Newton's iterative method to the polynomial f (x) D x n a, where n is a positive integer, to show that if x1 is an approximation to pn a, then x2 D (n 1)x1 C a=x n1 1 n is a better approximation and so on. (b) Find p3 2 correct to ve decimal places. [Hint: Take x1 D 1 as a rst approximation and use part (a).]

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