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Math Help - complex limit question

  1. #1
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    complex limit question

    \lim_{y->\infty}=\frac{e^{-y}+e^{y}}{y-y^3}=\infty

    i cant see how to prove that it goes infinity

    one way of thinking is:
    the numerator growes faster then the denominator

    the other is if we break e^x into taylor series
    an devide by the denominator and the result goes to infinity

    is there other way of proving the result?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by transgalactic View Post
    \lim_{y->\infty}=\frac{e^{-y}+e^{y}}{y-y^3}=\infty

    i cant see how to prove that it goes infinity

    one way of thinking is:
    the numerator growes faster then the denominator

    the other is if we break e^x into taylor series
    an devide by the denominator and the result goes to infinity

    is there other way of proving the result?
    Uh... \frac{e^{-y}+e^y}{y+y^3}\geqslant\frac{e^y}{2y^3}
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