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Find (4t + 1)u(t-1)} e-5(55+4) s² a. b. C. d. O Ob OC Od 3e-s 5² S e $(5s + 1) s² e-5(55-4) 5²

Find (4t + 1)u(t-1)} e-5(55+4) s² a. b. C. d. O Ob OC Od 3e-s 5² S e $(5s + 1) s² e-5(55-4) 5²

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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8. as soon as possible please

**Problem Statement:** Find the Laplace transform \( \mathcal{L}\{(4t + 1)\mu(t - 1)\} \). **Options:** a. \( \frac{e^{-5}(5s + 4)}{s^2} \) b. \( \frac{3e^{-5}}{s^2} + \frac{e^{-5}}{5} \) c. \( \frac{e^{-5}(5s + 1)}{s^2} \) d. \( \frac{e^{-5}(5s - 4)}{s^2} \) **Answer Choices:** ⊙ a ⊙ b ⊙ c ⊙ d **Explanation:** In this problem, you are asked to find the Laplace transform of the function \((4t+1)\mu(t-1)\), where \(\mu(t-1)\) is the Heaviside (or unit step) function. The correct expression will match one of the provided options. Be sure to apply the properties of the Laplace transform, including handling of the unit step function and any necessary shifting properties. **Note:** There are no graphs or diagrams in this problem. The content is straightforward and purely textual.
Transcribed Image Text:**Problem Statement:** Find the Laplace transform \( \mathcal{L}\{(4t + 1)\mu(t - 1)\} \). **Options:** a. \( \frac{e^{-5}(5s + 4)}{s^2} \) b. \( \frac{3e^{-5}}{s^2} + \frac{e^{-5}}{5} \) c. \( \frac{e^{-5}(5s + 1)}{s^2} \) d. \( \frac{e^{-5}(5s - 4)}{s^2} \) **Answer Choices:** ⊙ a ⊙ b ⊙ c ⊙ d **Explanation:** In this problem, you are asked to find the Laplace transform of the function \((4t+1)\mu(t-1)\), where \(\mu(t-1)\) is the Heaviside (or unit step) function. The correct expression will match one of the provided options. Be sure to apply the properties of the Laplace transform, including handling of the unit step function and any necessary shifting properties. **Note:** There are no graphs or diagrams in this problem. The content is straightforward and purely textual.
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