Program Explanation Given information: The function is F ( s ) = 1 ( s 4 − 16 ) . Explanation: The given function is F ( s ) = 1 ( s 4 − 16 ) . Apply inverse Laplace transform to the function F ( s ) = 1 ( s 4 − 16 ) . L − 1 { F ( s ) } = L − 1 { 1 ( s 4 − 16 ) } = L − 1 { 1 ( s 4 − 2 4 ) } = L − 1 { 1 ( s 2 − 2 2 ) ( s 2 + 2 2 ) } = L − 1 { 1 ( ( s − 2 ) ( s + 2 ) ) ( s 2 + 4 ) } Apply partial fraction method to solve the above expression, 1 ( ( s − 2 ) ( s + 2 ) ) ( s 2 + 4 ) = A s + B ( s 2 + 4 ) + C ( s + 2 ) + D ( s − 2 ) …… (1) Multiply the equation by denominator as, ( ( s − 2 ) ( s + 2 ) ) ( s 2 + 4 ) ( ( s − 2 ) ( s + 2 ) ) ( s 2 + 4 ) = [ ( A s + B ) ( ( ( s − 2 ) ( s + 2 ) ) ( s 2 + 4 ) ) ( s 2 + 4 ) + C ( ( s + 2 ) ( s 2 + 4 ) ) ( s + 2 ) + D ( ( s − 2 ) ( s + 2 ) ( s 2 + 4 ) ) ( s − 2 ) ] 1 = [ ( A s + B ) ( ( ( s − 2 ) ( s + 2 ) ) ) + C ( ( s − 2 ) ( s 2 + 4 ) ) + D ( ( s − 2 ) ( s 2 + 4 ) ) ] Substitute − 2 for s in above equation

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., Penney, David, Calvis

Publisher: PEARSON

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

Question

Chapter 7.3, Problem 17P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=1(s4−16) by using partial fraction.

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Chapter 7.3, Problem 16P

Chapter 7.3, Problem 18P

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Chapter 7 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F ( s ) = 1 ( s 4 − 16 ) by using partial fraction.

Solution Summary: The author explains how to obtain the inverse Laplace transformation of the functions by using partial tion.

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=1(s4−16) by using partial fraction.

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Chapter 7 Solutions