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Math Help - Multiplying/Dividing Power Series

  1. #1
    Senior Member mollymcf2009's Avatar
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    Multiplying/Dividing Power Series

    Use multiplication or division of power series to find the first 3 non-zero terms in the Maclaurin series for:

    e^{-9x^2} cos(4x)

    \sum^{\infty}_{n=0} \frac{(-9x^2)^n}{n!}

    = 1 - 9x^2 + \frac{81x^4}{2} - ...


    \sum^{\infty}_{n=0} (-1)^n \frac{(4x)^{2n}}{(2n)!}

    = 1 - \frac{16x^2}{2} + \frac{256x^4}{4} - ...


    \left(1 - 9x^2 + \frac{81x^4}{2}\right) \cdot \left(1 - \frac{16x^2}{2} + \frac{256x^4}{4}\right)

    I multiplied and got:

    1 - \frac{34x^2}{2} + \frac{706x^4}{4}

    which is not right in webassign. Should I have divided? Or what am I doing wrong?
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    looks like a mistake in your expansion for \cos(4x) ... forget the factorial?

    \cos(4x) \approx 1 - \frac{(4x)^2}{2!} + \frac{(4x)^4}{4!}<br />

    \cos(4x) \approx 1 - 8x^2 + \frac{32x^4}{3}
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  3. #3
    MHF Contributor Calculus26's Avatar
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    in your expansion for cos(4x) the coefficient for the x^4 term should be 32/3

    your method is correct
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