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Math Help - limits with e^x

  1. #1
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    limits with e^x

    lim e^(-1/x)/x
    x-> 0

    lim e^(-1/x)/x
    x-> infinity


    i keep getting that they do not exist, and i need an actual value.
    No idea what im doing wrong, any help much appreciated.
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  2. #2
    Junior Member
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    first one looks like..

    approaching infinity / approaching zero, which just boosts the infinity into more infinitiness ;D

    so its infinity..

    it looks that way to me anyways without writing it down..

    second one looks like...

    top goes to 1/ bottom is x as x approaches infinity which would make it zero.
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  3. #3
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    ok, thanks, so im not completely out of it!!

    It turns out i reduced my equation incorrectly. So im actually getting an answer instead of infinity now! YAY!!
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  4. #4
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    was I right?
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  5. #5
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    If you let u= 1/x your limits become \lim_{u\rightarrow \infty} ue^{-u} and \lim_{u\rightarrow 0}ue^{-u}. The second of those is easy: setting u= 0 we get 0(1)= 0. For the first, you need to know that an exponential "dominates" and polynomial. e^{-x} goes to 0 "faster" than u goes to infinity.
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