Explanation Given information: The function is expressed as shown below: f ( x ) = x 4 − 8 x 2 − 128 Proof: The given function f ( x ) is the polynomial of order 4 . To obtain the solution of the function, equate the function f ( x ) as 0. x 4 − 8 x 2 − 128 = 0 …… (1) Consider t as x 2 in the function f ( x ) . t = x 2 Substitute t for x 2 in the equation (1) as follows: t 2 − 8 t − 128 = 0 Factorize the above function as follows: t 2 − 16 t + 8 t − 128 = 0 t ( t − 16 ) + 8 ( t − 16 ) = 0 ( t − 16 ) ( t + 8 ) = 0 Use zero product property in the above equation, to obtain the value of t

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 4.2, Problem 76E

To determine

To prove:

The greatest root of the function ..is x=4.

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Chapter 4.2, Problem 75E

Chapter 4.2, Problem 77E

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Examples: Solve the following differential equation using Laplace transform (e) ty"-ty+y=0 with y(0) = 0, and y'(0) = 1

Examples: Solve the following differential equation using Laplace transform (a) y" +2y+y=t with y(0) = 0, and y'(0) = 1

Chapter 4 Solutions

Calculus: Early Transcendentals

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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