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February 26th, 2012, 09:11 PM   #1
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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^3-33*x-66 .


x1=?
lx1?x0l=?

x2=?
lx2?x1l= ?

x3=?
lx3?x2l=?
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February 26th, 2012, 09:50 PM   #2
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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\(8^2-11\)}=\frac{1090}{159}" />









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February 29th, 2012, 12:28 AM   #3
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Re: Newton's Method?

Thank you!
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