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Math Help - Another Taylor series

  1. #1
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    Another Taylor series

    Let .
    Find the MacLaurin polynomial of degree 5 for .


    i know that this can be solved by using this as a base


    then I would just plug in (-2t^4) in place of x and expand it to 5th degree.

    then I think I messed up here.

    Please need help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fastcarslaugh View Post
    Let .
    Find the MacLaurin polynomial of degree 5 for .


    i know that this can be solved by using this as a base


    then I would just plug in (-2t^4) in place of x and expand it to 5th degree.

    then I think I messed up here.

    Please need help.
    Not quite, you need to observe that:

    F'(x)=e^{-2x^4}

    Then use the series expansion of e^x to expand this , then integrate term by term to get the desired series.

    CB
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  3. #3
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    I seem to be integrating this incorrectly..
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  4. #4
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    e^u = 1 + u + \frac{u^2}{2!} + \frac{u^3}{3!} + ...

    e^{-2t^4} \approx 1 - 2t^4

    F(x) \approx \int_0^x  1 - 2t^4 \, dt = \left[t - \frac{2}{5}t^5\right]_0^x = x - \frac{2}{5}x^5
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