## Laplace transform limits?

How we get relation
$$\lim_{t\to 0}f(t)=\lim_{p\to \infty}pF(p)$$?

Where ##\mathcal{L}\{f\}=F##.
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 Recognitions: Science Advisor 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.
 I saw also assymptotics relation ##\lim_{t \to \infty}f(t)=\lim_{p\to 0}pF(p)## when that relation is valid?

Recognitions: