# Laplace transform limits?

1. Nov 19, 2012

### matematikuvol

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

Where $\mathcal{L}\{f\}=F$.

2. Nov 19, 2012

### mathman

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.

3. Nov 22, 2012

### matematikuvol

I saw also assymptotics relation
$\lim_{t \to \infty}f(t)=\lim_{p\to 0}pF(p)$
when that relation is valid?

4. Nov 22, 2012

### mathman

I am not familiar with this. However for most cases, both sides = 0.

5. Nov 23, 2012

### matematikuvol

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.