Let f(x) := sin(x²) and let f(x) f'(x) g(x) := x %3D be the Newton's method iteration function. (a) Show that Newton's method converges linearly for this function. (b) Now consider a modified Newton's method: 91(x) : 2f (x) f'(x)' = T - Show that, for this modified Newton's method, convergence is (at least) quadratic.

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