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Laplace transform limits?

  1. Nov 19, 2012 #1
    How we get relation
    [tex]\lim_{t\to 0}f(t)=\lim_{p\to \infty}pF(p)[/tex]?

    Where ##\mathcal{L}\{f\}=F##.
     
  2. jcsd
  3. Nov 19, 2012 #2

    mathman

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    pF(p) = p∫e-ptf(t)dt. Integrate by parts with du = pe-ptdt and v = f(t). Then (assuming f(t) reasonable) let p -> ∞ and you get the desired result.
     
  4. Nov 22, 2012 #3
    I saw also assymptotics relation
    ##\lim_{t \to \infty}f(t)=\lim_{p\to 0}pF(p)##
    when that relation is valid?
     
  5. Nov 22, 2012 #4

    mathman

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    I am not familiar with this. However for most cases, both sides = 0.
     
  6. Nov 23, 2012 #5
    For ##1## both sides are equal ##1##. ##lim_{t\to \infty}1=1=lim_{p\to 0}p\frac{1}{p}=1##. I think that is correct only if both limits converge.
     
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