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Math Help - limit with products of n and e

  1. #1
    Junior Member
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    limit with products of n and e

    find the limit of n^2*e^{-n} as n approaches infinity

    I just dont see how to do limits of more complex things. I can take each part by itself, find its limit and multiply them by algebra rules of limits. But n^2 = infinity and e^-n = 0. That does not work. L'Hop rule does not work either.

    I am really confused on how to do limits.
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Hello.

    Quote Originally Posted by diroga View Post
    find the limit of n^2*e^{-n} as n approaches infinity

    I just dont see how to do limits of more complex things. I can take each part by itself, find its limit and multiply them by algebra rules of limits. But n^2 = infinity and e^-n = 0. That does not work. L'Hop rule does not work either.

    I am really confused on how to do limits.
    Of course L'Hospital works perfectly.

    n^2*e^{-n}  = \frac{n^2}{e^n}

    Using L'Hospital leeds to

    lim \frac{n^2}{e^n} = lim \frac{2n}{e^n} = lim \frac{2}{e^n}


    Can you see it now?

    Regards
    Rapha
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  3. #3
    Junior Member
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    Apr 2009
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    :-/

    yeah... 0

    thx.
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