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SOLVED:The function f(x)=(x-1)^2 e^x has a double root at x=1. (a) Derive Newton's iteration for this function. Show that the iteration is well-defined so long as xk ≠-1 and that the convergence rate is expected to be similar to that of the bisection method (and certainly not quadratic). (b) Implement Newton's method and observe its performance starting from x0=2. (c) How easy would it be to apply the bisection method? Explain.
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