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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 41E
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**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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