Laplace Growth restriction

  • Thread starter KateyLou
  • Start date
  • #1
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Homework Statement


The condition to be satisfied for a Laplace transform is U(t)<Mekt


Homework Equations


I am trying to proove that et2 does not satisfy this


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?!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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.
 
  • #3
17
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YAY! Thank you!
 

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