February 26th, 2012, 09:11 PM  #1 
Newbie Joined: Feb 2012 Posts: 10 Thanks: 0  Newton's Method?
Use Newton's method to approximate the root of the equation x^3=33x+66 that belongs to the interval (4,. Start with x0=8 and perform three iterations, i.e., find x1, x2, and x3. Calculate lx0?x1l lx1?x2l , and lx3?x2l . Answers: 1. Use Newton's method xn+1=xn? f(xn) / f (xn) where the function f has a positive leading coefficient so that f(x)= x^333*x66 . x1=? lx1?x0l=? x2=? lx2?x1l= ? x3=? lx3?x2l=? 
February 26th, 2012, 09:50 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Newton's Method?
First, express the equation as a function equal to zero: Calculate the function's first derivative: Newton's method gives us the recursion: With we find: 66}{3\(8^211\)}=\frac{1090}{159}" /> 
February 29th, 2012, 12:28 AM  #3 
Newbie Joined: Feb 2012 Posts: 10 Thanks: 0  Re: Newton's Method?
Thank you!


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