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Math Help - Maclaurin Approximation

  1. #1
    Filthypeasant
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    Maclaurin Approximation

    How would you determine the degree of the Maclaurin polynomial required for the error in the approximation to be less than 0.0001 for
    f(x)=cos(pi*x^2) approximating f(0.6)? Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Filthypeasant
    How would you determine the degree of the Maclaurin polynomial required for the error in the approximation to be less than 0.0001 for
    f(x)=cos(pi*x^2) approximating f(0.6)? Thanks!
    Look at the form of the remainder of the Maclaurin polynomial. Set if to be
    less than 0.0001 then solve to find the minimum degree that satisfies
    the inequality. This may need to be done by trial and error.

    And it looks to me as though the required degree is 16.

    Look at the post on Taylor polynomials just below this one for more details.

    RonL
    Last edited by CaptainBlack; February 27th 2006 at 03:39 AM.
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