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...
icon
Related questions
Question
**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 \( f(t) \).
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 \( f(t) \).
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning