Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Use Definition 7.1.1** **DEFINITION 7.1.1 Laplace Transform** Let \( f \) be a function defined for \( t \geq 0 \). Then the integral \[ \mathcal{L}\{f(t)\} = \int_{0}^{\infty} e^{-st}f(t) \, dt \] is said to be the *Laplace transform* of \( f \), provided that the integral converges. To find \(\mathcal{L}\{f(t)\}\). (Write your answer as a function of \( s \).) \( f(t) = te^{7t} \) \[ \mathcal{L}\{f(t)\} = \quad \text{(s > 7)} \] --- **Use Theorem 7.1.1 to find \(\mathcal{L}\{f(t)\}\). (Write your answer as a function of \( s \).)** \( f(t) = 8t^4 \) \[ \mathcal{L}\{f(t)\} = \]
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Transcribed Image Text:**Use Definition 7.1.1** **DEFINITION 7.1.1 Laplace Transform** Let \( f \) be a function defined for \( t \geq 0 \). Then the integral \[ \mathcal{L}\{f(t)\} = \int_{0}^{\infty} e^{-st}f(t) \, dt \] is said to be the *Laplace transform* of \( f \), provided that the integral converges. To find \(\mathcal{L}\{f(t)\}\). (Write your answer as a function of \( s \).) \( f(t) = te^{7t} \) \[ \mathcal{L}\{f(t)\} = \quad \text{(s > 7)} \] --- **Use Theorem 7.1.1 to find \(\mathcal{L}\{f(t)\}\). (Write your answer as a function of \( s \).)** \( f(t) = 8t^4 \) \[ \mathcal{L}\{f(t)\} = \]
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