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9. Laplace Transforms (a) Use the integral definition to find L{cosh(t). e}. Use the nspire to integrate (b) Use the shortcut formulas to find L{8tª −5t² −2+3 sin(5t)}

9. Laplace Transforms (a) Use the integral definition to find L{cosh(t). e}. Use the nspire to integrate (b) Use the shortcut formulas to find L{8tª −5t² −2+3 sin(5t)}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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# Laplace Transforms ## Exercises: ### 9. Laplace Transforms #### (a) Task: Use the integral definition to find the Laplace Transform of the function \( \mathcal{L} \{ \cosh(t) \cdot e^{-t} \} \). Hint: Use the nspire calculator to integrate. #### (b) Task: Utilize the shortcut formulas to find the Laplace Transform of the function \( \mathcal{L} \{ 8t^4 - 5t^2 - 2 + 3\sin(5t) \} \). **Note:** There are no graphs or diagrams accompanying these tasks.
Transcribed Image Text:# Laplace Transforms ## Exercises: ### 9. Laplace Transforms #### (a) Task: Use the integral definition to find the Laplace Transform of the function \( \mathcal{L} \{ \cosh(t) \cdot e^{-t} \} \). Hint: Use the nspire calculator to integrate. #### (b) Task: Utilize the shortcut formulas to find the Laplace Transform of the function \( \mathcal{L} \{ 8t^4 - 5t^2 - 2 + 3\sin(5t) \} \). **Note:** There are no graphs or diagrams accompanying these tasks.
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