Does et^2 Satisfy the Growth Restriction for Laplace Transform?

[KateyLou]

Homework Statement

The condition to be satisfied for a Laplace transform is U(t)<Me^kt

Homework Equations

I am trying to proove that e^t2 does not satisfy this

The Attempt at a Solution

It was suggested that we try taking logarithms of both side:
t²<ln(Me^kt)
t²<lnM+lne^kt
t²<lnM+kt
t²-kt<ln M

I don't think this shows anything?!

 

[Dick]

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.

 

[KateyLou]

YAY! Thank you!