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Math Help - Asymptotes

  1. #1
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    Asymptotes

    f(x) = xe^{-x}

    Looking at the equation, the Domain of the function should be all reals, but when I graph it on my calculator, there appears to be a horizontal asymptote right above zero and a vertical asymptote somewhere in the 3rd quadrant (the function suggests that y should continue to grow smaller (more negative) on into infinity, but it's like the paradox of in order to move from a to b, you must first move half way there, and half way to half way, and so on).

    How do I find the asymptotes algebraically?
    Last edited by mr fantastic; April 7th 2009 at 03:11 PM. Reason: Fixed the latex
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  2. #2
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    See this for example.
    Attached Thumbnails Attached Thumbnails Asymptotes-x.e_-x.png  
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  3. #3
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    Quote Originally Posted by tom ato View Post
    f(x) = xe^{-x}

    Looking at the equation, the Domain of the function should be all reals, but when I graph it on my calculator, there appears to be a horizontal asymptote right above zero and a vertical asymptote somewhere in the 3rd quadrant (the function suggests that y should continue to grow smaller (more negative) on into infinity, but it's like the paradox of in order to move from a to b, you must first move half way there, and half way to half way, and so on).

    How do I find the asymptotes algebraically?
    There is only one asymptote and that is a horizontal asymptote. You find it by considering the limit of the function as x --> +oo.

    There is no vertical asymptote because there is no value of x for which the function is not defined.
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