Initial Value Theorem (IVT)

Theorem 2: Initial Value theorem

If $f(t)$ is piecewise-continuous and ${\int }_0^{\infty }|f(t)|e^{-\alpha t}dt$ converges for some $\alpha \in \mathbb{R}$ then

$f(0^{+})={\lim }_{s\to +\infty }sF(s)$

Related

• Initial Value Problem
• Final Value Theorem