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A limit

  1. Mar 10, 2008 #1

    quasar987

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    [SOLVED] A limit

    1. The problem statement, all variables and given/known data
    How do you show that

    [tex]\lim_{x\rightarrow a}\frac{e^{-a^2/(a^2-x^2)}}{(a^2-x^2)^{2m}(x-a)}=0[/tex]

    for 'm' a positive integer and 'a' a real number >0??


    This is a type 0/0 indeterminate form but l'Hospital's rule is not helpful because when you differentiate the denominator, you make the degree 4m+1 polynomial of the denominator drop 1 degree, but you make a (-2xa²)/(a²-x²)² appear in the numerator.

    And Mapple says "undefined" when I plug a=3 :grumpy:
     
    Last edited: Mar 10, 2008
  2. jcsd
  3. Mar 10, 2008 #2

    StatusX

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    Try a change of variables.
     
    Last edited: Mar 10, 2008
  4. Mar 11, 2008 #3

    quasar987

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    It seems I tried every change of variable possible but none help... :/
     
  5. Mar 11, 2008 #4

    StatusX

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    How about taking your new variable to be whats in the exponential. You'll be left with something like:

    [tex] \lim_{u \rightarrow \infty} e^{-u} p(u) f(u) [/tex]

    where p(u) is a polynomial, and f(u) is something that looks like a polynomial for large u. It shouldn't be too hard from here.
     
  6. Mar 12, 2008 #5

    quasar987

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    Got it. I had made an error in calculating.

    Thanks StatusX.
     
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