Final Value Theorem of Laplace Transform/Examples/Example 1
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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: $27 \ \text{(b)}$