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Laplace Growth restriction

  1. Dec 21, 2008 #1
    1. The problem statement, all variables and given/known data
    The condition to be satisfied for a Laplace transform is U(t)<Mekt


    2. Relevant equations
    I am trying to proove that et2 does not satisfy this


    3. The attempt at a solution
    It was suggested that we try taking logarithms of both side:
    t2<ln(Mekt)
    t2<lnM+lnekt
    t2<lnM+kt
    t2-kt<ln M

    I dont think this shows anything?!
     
  2. jcsd
  3. Dec 21, 2008 #2

    Dick

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    Sure it shows something. t^2-kt is unbounded as t->infinity. ln(M) is a constant. t^2-kt<ln(M) can't be true for all t.
     
  4. Dec 21, 2008 #3
    YAY! Thank you!
     
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