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Math Help - Finding a limit using Maclaurin Series

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    Finding a limit using Maclaurin Series

    Hi,

    I having trouble understanding how to use the Maclaurin series on this question. I would be thankful if someone could give me nudge in the right direction.

    Use the Maclaurin series to evaluate the limit

    \lim {(x \to 0)}\ \frac{e^{x}\sin{x} - x - x^2}{x^3}

    Thanks for any help.
    Last edited by mr fantastic; November 2nd 2009 at 02:25 AM. Reason: Changed post title
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    Quote Originally Posted by Beard View Post
    Hi,

    I having trouble understanding how to use the Maclaurin series on this question. I would be thankful if someone could give me nudge in the right direction.

    Use the Maclaurin series to evaluate the limit

    \lim {(x \to 0)}\ \frac{e^{x}\sin{x} - x - x^2}{x^3}

    Thanks for any help.
    Substitute the first two terms of the Maclaurin Series for sin x and e^x, expand, simplify and divide numerator and denominator by the obvious common factor. Then take the limit. (Apart from doing all this, your job is also to think about why only the first two terms are necessary).
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