If L [f(t)] = F(s), then the initial value theorem for Laplace transform is:
1
\(\mathop {\lim }\limits_{t \to 0} f\left( t \right) = \mathop {{\rm{lim}}}\limits_{s \to \infty } F\left( s \right)\)
2
\(\mathop {{\rm{lim}}}\limits_{t \to \infty } \;f\left( t \right) = \mathop {{\rm{lim}}}\limits_{s \to 0} \;F\left( s \right)\)
3
\(\mathop {{\rm{lim}}}\limits_{t \to 0} \;f\left( t \right) = \mathop {{\rm{lim}}}\limits_{s \to \infty } \;sF\left( s \right)\)
4
\(\mathop {{\rm{lim}}}\limits_{t \to 0} \;f\left( t \right) = \mathop {{\rm{lim}}}\limits_{s \to 0} \;sF\left( s \right)\)