Find the inverse Laplace transform f(t) of F(s) = (s+1)(s – 3)(s – 4) First find the partial fraction expansion A F(s): B C (s+1) - 3) (s – 4) A= -6 B -31 C = f(t -
Find the inverse Laplace transform f(t) of F(s) = (s+1)(s – 3)(s – 4) First find the partial fraction expansion A F(s): B C (s+1) - 3) (s – 4) A= -6 B -31 C = f(t -
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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![**Problem:**
Find the inverse Laplace transform \( f(t) \) of
\[
F(s) = \frac{6s^2 - 31s + 23}{(s+1)(s-3)(s-4)}
\]
**Step:**
First, find the partial fraction expansion.
\[
F(s) = \frac{A}{(s+1)} + \frac{B}{(s-3)} + \frac{C}{(s-4)}
\]
**Calculations:**
- \( A = -6 \)
- \( B = -31 \)
- \( C = \) [Blank for user input]
- \( f(t) = \) [Blank for user input]
The goal is to solve for \( C \) and then use the values to write \( f(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8edd889e-338a-4275-872c-5b2b400b4e22%2F4d076e03-206a-4925-8deb-83df84bbe268%2Fbzpaela_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the inverse Laplace transform \( f(t) \) of
\[
F(s) = \frac{6s^2 - 31s + 23}{(s+1)(s-3)(s-4)}
\]
**Step:**
First, find the partial fraction expansion.
\[
F(s) = \frac{A}{(s+1)} + \frac{B}{(s-3)} + \frac{C}{(s-4)}
\]
**Calculations:**
- \( A = -6 \)
- \( B = -31 \)
- \( C = \) [Blank for user input]
- \( f(t) = \) [Blank for user input]
The goal is to solve for \( C \) and then use the values to write \( f(t) \).
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