1. Let f(x) = (ra)g(r) where m 2 is an integer and g(r) C(R), g(a)...

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1. Let f(x) = (ra)"g(r) where m≥ 2 is an integer and g(r) € C²(R), g(a) ‡ 0. Write down the Newton's method for finding the root a of f(x), and study the order of convergence for the method. Can you propose a method that converges faster? 1. Let f(x) = (ra)"g(r) where m≥ 2 is an integer and g(r) € C²(R), g(a) ‡ 0. Write down the Newton's method for finding the root a of f(x), and study the order of convergence for the method. Can you propose a method that converges faster?