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Find the given inverse Laplace transform. e-¹_5 s²-5s) a. 5+5e-5t b. 1-e(-5/2)t c. −1+e5t d. 5-5e5t e. 1-le-5t

Find the given inverse Laplace transform. e-¹_5 s²-5s) a. 5+5e-5t b. 1-e(-5/2)t c. −1+e5t d. 5-5e5t e. 1-le-5t

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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# Finding the Inverse Laplace Transform To determine the inverse Laplace transform of a given function, let's consider the following problem: ## Problem Find the given inverse Laplace transform: \[ \mathcal{L}^{-1} \left\{ \frac{5}{s^2 - 5s} \right\} \] ### Options a. \(5 + 5e^{-5t}\) b. \(1 - e^{\left( -\frac{5}{2} \right)t}\) c. \(-1 + e^{5t}\) d. \(5 - 5e^{5t}\) e. \(1 - 1e^{-5t}\) ### Explanation To solve this, follow these steps: 1. **Simplify the Laplace expression:** Break down the given function into simpler partial fractions if possible. 2. **Identify the standard Laplace transforms:** Use known inverse Laplace transforms to find the solution. 3. **Combine the results to get the final inverse Laplace transform.** This is a multiple-choice question asking for the correct inverse Laplace transform among several given options.
Transcribed Image Text:# Finding the Inverse Laplace Transform To determine the inverse Laplace transform of a given function, let's consider the following problem: ## Problem Find the given inverse Laplace transform: \[ \mathcal{L}^{-1} \left\{ \frac{5}{s^2 - 5s} \right\} \] ### Options a. \(5 + 5e^{-5t}\) b. \(1 - e^{\left( -\frac{5}{2} \right)t}\) c. \(-1 + e^{5t}\) d. \(5 - 5e^{5t}\) e. \(1 - 1e^{-5t}\) ### Explanation To solve this, follow these steps: 1. **Simplify the Laplace expression:** Break down the given function into simpler partial fractions if possible. 2. **Identify the standard Laplace transforms:** Use known inverse Laplace transforms to find the solution. 3. **Combine the results to get the final inverse Laplace transform.** This is a multiple-choice question asking for the correct inverse Laplace transform among several given options.
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