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Math Help - Series Help!

  1. #1
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    Series Help!

    Find the Maclaurin series of
    f(x)=(1+x^2)^(2/3)
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  2. #2
    MHF Contributor

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    f(0)= 1

    f'(x)= (2/3)(x^2+ 1)^{1/3}(2x)= (4/3)x(x^2+ 1)^{1/3} so f'(0)= 0.

    f"(x)= (4/3)(x^2+ 1)^{1/3}+ (8/9)x^2(x^+ 1)^{-2/3} so f"(0)= 4/3.

    Keep going until you see a pattern.
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