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Laplace transform limits?

by matematikuvol
Tags: laplace, limits, transform
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matematikuvol
#1
Nov19-12, 10:00 AM
P: 192
How we get relation
[tex]\lim_{t\to 0}f(t)=\lim_{p\to \infty}pF(p)[/tex]?

Where ##\mathcal{L}\{f\}=F##.
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mathman
#2
Nov19-12, 03:08 PM
Sci Advisor
P: 6,077
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.
matematikuvol
#3
Nov22-12, 03:16 AM
P: 192
I saw also assymptotics relation
##\lim_{t \to \infty}f(t)=\lim_{p\to 0}pF(p)##
when that relation is valid?

mathman
#4
Nov22-12, 03:55 PM
Sci Advisor
P: 6,077
Laplace transform limits?

Quote Quote by matematikuvol View Post
I saw also assymptotics relation
##\lim_{t \to \infty}f(t)=\lim_{p\to 0}pF(p)##
when that relation is valid?
I am not familiar with this. However for most cases, both sides = 0.
matematikuvol
#5
Nov23-12, 02:05 AM
P: 192
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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