Final 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:

$\map f t = 3 e^{-2 t}$

From Laplace Transform of Exponential:

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

Then by the Initial Value Theorem of Laplace Transform:

\(\ds \lim_{t \mathop \to 0} 3 e^{-2 t}\)

\(=\)

\(\ds \lim_{s \mathop \to \infty} \dfrac 3 {s + 2}\)

\(\ds \leadsto \ \ \)

\(\ds 3\)

\(=\)

\(\ds 3\)

Sources

• 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Solved Problems: Initial and Final Value Theorems: $27 \ \text{(b)}$