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Math Help - Maclaurin and mean value help

  1. #1
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    Unhappy Maclaurin and mean value help

    Hi All
    i would really appreciate any help on the following problems

    1. Maclaurin expansion of lncosx up to x^4.

    2. Mean value of y= 2e^x/3 between x=3 and x=6.

    Thanks
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  2. #2
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    Quote Originally Posted by bhav View Post
    Hi All
    i would really appreciate any help on the following problems

    1. Maclaurin expansion of lncosx up to x^4.

    2. Mean value of y= 2e^x/3 between x=3 and x=6.

    Thanks
    1. Do you know the formula for the nth term in a Maclaurin series? It is in your class notes and textbook. Where are you stuck in applying it?

    2. By definition (the one that is in your class notes and textbook): \displaystyle \frac{\int_{3}^{6} \frac{2 e^x}{3} \, dx}{6 - 3}
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  3. #3
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    First, note that

    \frac{d}{dx}[\ln{(\cos{x})}] = \tan{x}

    so \ln{(\cos{x})} = \int{\tan{x}\,dx}.


    So if you can find a Maclaurin series for \tan{x}, integrate it and then you have the Maclaurin series for \ln{(\cos{x})}.
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