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Math Help - Mclaurin Series.

  1. #1
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    Mclaurin Series.

    The question is: . Find the Maclaurin series of f (x) = (1 + x^2)^(3/2)
    Not sure where to start I think you might have to use the formula (1+a)^k.. but still don't know what to do
    Last edited by calculuskid1; March 24th 2010 at 05:02 PM. Reason: Spelling Error
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  2. #2
    MHF Contributor chisigma's Avatar
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    Binomial Series -- from Wolfram MathWorld

    Kind regards

    \chi \sigma
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  3. #3
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    The Maclaurin series is a Taylor series around x=0:

    f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^n

    where f^{(n)}(0) is the n-th derivative of f(x) evaluated at x=0. To get an expression for the n-th derivative, it usually works to do the first 3 or 4 and you start to see a pattern. Then you can write f^{(n)}(x) and take the derivative to make sure it matches f^{(n+1)}(x).

    In some cases, you can just take the first few derivatives and write your answer like:

    f(x)=f(0)+f'(0)x+\frac{f''(0)}{2}x^2+\frac{f'''(0)  }{6}x^3+...

    with the correct values substituted, of course.

    Post again in this thread if you're still having trouble.
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