# Initial Value Theorem (IVT)

Theorem 2: Initial Value theorem

If $f(t)$ is piecewise-continuous and $∫_{0}∣f(t)∣e_{−αt}dt$ converges for some $α∈R$ then

$f(0_{+})=lim_{s→+∞}sF(s)$

Theorem 2: Initial Value theorem

If $f(t)$ is piecewise-continuous and $∫_{0}∣f(t)∣e_{−αt}dt$ converges for some $α∈R$ then

$f(0_{+})=lim_{s→+∞}sF(s)$