# Initial Value Theorem of Laplace Transform/Examples/Example 1

## Example of use of Initial Value Theorem of Laplace Transform

Consider the real function $f: \R \to \R$ defined as:

$\map f t = 3 e^{-2 t}$
$\laptrans {\map f t} = \dfrac 3 {s + 2}$

Then by the Initial Value Theorem of Laplace Transform:

 $\ds \lim_{t \mathop \to 0} 3 e^{-2 t}$ $=$ $\ds \lim_{s \mathop \to \infty} \dfrac 3 {s + 2}$ $\ds \leadsto \ \$ $\ds 3$ $=$ $\ds 3$