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Math Help - Maclauren polynomials

  1. #1
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    Maclauren polynomials

    A couple of problems:

    1. Find the Maclauren Polynomial of degree 4 for the function f(x) = x/(x+1)

    2. Determine the degree of the Maclauren polynomial required for the error in the approximation of the function, f(x) = cos(x) to be less than 0.001, if x=0.1

    Thanks!
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  2. #2
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    Quote Originally Posted by bakanagaijin View Post
    A couple of problems:

    1. Find the Maclauren Polynomial of degree 4 for the function f(x) = x/(x+1)
    Do you know the definition of a Maclaurin series? If yes show us what you have done.

    2. Determine the degree of the Maclauren polynomial required for the error in the approximation of the function, f(x) = cos(x) to be less than 0.001, if x=0.1
    Because the series for cos has alternating signs the error for x=0.001 is less than the first neglected term. Alternativley use one of the remainder formulas for Taylor series.

    RonL
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  3. #3
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    Quote Originally Posted by bakanagaijin View Post
    A couple of problems:

    1. Find the Maclauren Polynomial of degree 4 for the function f(x) = x/(x+1)

    2. Determine the degree of the Maclauren polynomial required for the error in the approximation of the function, f(x) = cos(x) to be less than 0.001, if x=0.1

    Thanks!
    utilizing the fact that only for x\in(-1,1) \frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^{n}x^{n} you can easily extrapolate the first answer by taking the product of that series and x...then expand until the desired order of polynomial is acheived
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