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Limits are plugged in terms become infinite

  1. Apr 3, 2009 #1
    1. The problem statement, all variables and given/known data

    find the integral from 0 to infinity of t^(-1)*e^(-st) dt

    2. Relevant equations

    e^x series expansion

    3. The attempt at a solution

    I expanded e^(-st) into its series and then integrated, it appears to diverge since when the limits are plugged in terms become infinite, but I am unsure since the series alternates with (-1)^n.
     
    Last edited: Apr 3, 2009
  2. jcsd
  3. Apr 3, 2009 #2

    Dick

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    Re: Intergral

    Sure it diverges. exp(-st) approaches 1 as t->0. So near 0 the integral diverges like 1/t. If s=0 it's exactly 1/t.
     
    Last edited: Apr 3, 2009
  4. Apr 3, 2009 #3
    Re: Intergral

    Is showing that the function has a diverging asymptote at one of the endpoints strong enough proof to say that it's integral diverges to +inf?
     
  5. Apr 3, 2009 #4

    Dick

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    Re: Intergral

    Sure. More formally write a comparison test for the integral on the interval of say t from 0 to 1/s. If it's greater than something that diverges, then it diverges.
     
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