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Math Help - Numerical Analysis: Newton's Method Problem

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    Numerical Analysis: Newton's Method Problem

    Use Newtons Method to find the solution accurate to within 10^-5 of the following problem.

    x^2-2xe^(-x)+e^(-2x)=0

    How do I know when to stop and how do I find P0 and P1?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by wvlilgurl View Post
    Use Newtons Method to find the solution accurate to within 10^-5 of the following problem.

    x^2-2xe^(-x)+e^(-2x)=0

    How do I know when to stop
    as the problem said, you want to be accurate to 5 decimal places, so keep finding a better approximation until the first 5 decimal places do not change


    and how do I find P0 and P1?
    i suppose you mean the initial guess?

    first note that you have (x - e^{-x})^2

    so a good initial guess would be one where x is close to e^{-x}. in fact, it is an equivalent problem to solve x - e^{-x} = 0. would be easier to run Newton's method on it too. you can use a graph to come up with a guess

    Hope that helps
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