# Real Analysis - Newton's Method and showing convergence.

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Newton's Method: Consider the equation f(x)=0 where f is a real-valued function of a real variable. Let x_0 be any initial approximation of the solution and let

x_(n+1)=x_n - (f(x_n)/f'(x_n)).

Show that if there is a positive number "a" such that for all x in [x_0-a, x_0+a]

|(f(x)f''(x))/((f'(x))^2)|<=lambda<1 and

|(f(x_0))/(f'(x_0))|<=(1-lamda)a

then the sequence (x_n) converges to a solution of f(x)=0.

https://brainmass.com/math/real-analysis/real-analysis-newtons-method-showing-convergence-87794

#### Solution Summary

Newton's Method and convergence are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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