# Limit to Infinity of Laplace Transform

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## Theorem

Let $\laptrans {\map f t} = \map F s$ denote the Laplace transform of the real function $f$.

Then:

- $\displaystyle \lim_{s \mathop \to \infty} \map F s = 0$

## Proof

## Sources

- 1965: Murray R. Spiegel:
*Theory and Problems of Laplace Transforms*... (previous) ... (next): Chapter $1$: The Laplace Transform: Some Important Properties of Laplace Transforms: $10$. Behavior of $\map f s$ as $s \to 0$: Theorem $1 \text{-} 15$