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Math Help - Newtons method help

  1. #1
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    Newtons method help

    Hey guys, need some help with this question. I am stuck and don't know what to do.

    Q: Show that using newton's method to 1-\frac{R}{x^n} and to x^n-R for determining (R)^{\frac{1}{n}} results in 2 similar, but different iterative formulas, with n \ge 2 and R >0

    Thanks for your help guys!
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  2. #2
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    May 2008
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    Re: Newtons method help

    Ok so Newton's method is a way of determining a root of the equation
    f(x)=0

    in both of the cases above for f(x) we obtain f(x) =0 \Rightarrow x = (R)^{1/n} so we just need to apply Newton's method.

    This works by calculating the tangent line at a point x_n finding where it intersects the x-axis and assuming that this gives a better approximation to the root than  x_n

    Graphically you can see it at work here
    http://upload.wikimedia.org/wikipedi...ration_Ani.gif

    Algebraically it is
    x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}

    A derivation can be found here Newton's method - Wikipedia, the free encyclopedia

    So work out the derivatives of the two functions you have above then plug it into the formula and you should have two iterative formulas which will converge on (R)^{1/n}
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