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Laplace transform limits? 
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#1
Nov1912, 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##. 


#2
Nov1912, 03:08 PM

Sci Advisor
P: 6,038

pF(p) = p∫e^{pt}f(t)dt. Integrate by parts with du = pe^{pt}dt and v = f(t). Then (assuming f(t) reasonable) let p > ∞ and you get the desired result.



#3
Nov2212, 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? 


#4
Nov2212, 03:55 PM

Sci Advisor
P: 6,038

Laplace transform limits?



#5
Nov2312, 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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