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Math Help - Finding New Taylor Series from Old Ones

  1. #1
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    Finding New Taylor Series from Old Ones

    Use a know taylor series to find the taylor series about c=0 for the given function and find its radius of convergence.

    f(x)=x sin(x)

    well, the taylor series for sin(x) is

    sin(x)= \sum\frac{-1^k}{2k+1!}x^{2k+1}

    So I know I plug in the x's, but I don't know which ones since there's one before and one inside of the sin function.
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  2. #2
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    Quote Originally Posted by kl.twilleger View Post
    Use a know taylor series to find the taylor series about c=0 for the given function and find its radius of convergence.

    f(x)=x sin(x)

    well, the taylor series for sin(x) is

    sin(x)= \sum\frac{-1^k}{2k+1!}x^{2k+1}

    So I know I plug in the x's, but I don't know which ones since there's one before and one inside of the sin function.
    You have:

    \sin(x)= \sum_{k=0}^{\infty}\frac{-1^k}{(2k+1)!}x^{2k+1}

    so:

    f(x)=x \sin(x)= \sum_{k=0}^{\infty}\frac{-1^k}{(2k+1)!}x^{2k+2}

    Now adjust the indices to taste.

    This has the same radius of convergence as the series for \sin(x)

    CB
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