# Laplace transform limits?

by matematikuvol
Tags: laplace, limits, transform
 P: 190 How we get relation $$\lim_{t\to 0}f(t)=\lim_{p\to \infty}pF(p)$$? Where ##\mathcal{L}\{f\}=F##.
 Sci Advisor P: 5,768 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.
 P: 190 I saw also assymptotics relation ##\lim_{t \to \infty}f(t)=\lim_{p\to 0}pF(p)## when that relation is valid?
P: 5,768

## Laplace transform limits?

 Quote by matematikuvol 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.
 P: 190 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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