Explanation Find the general solution of each of the given equations and obtain the value when the limit lim t → ∞ y ( t ) is applied. Given: (a) d y d t = − 4 ( y − 12 ) (b) d y d t = 4 ( y − 12 ) (c) d y d t = − 4 y − 12 Calculation: (a) d y d t = − 4 ( y − 12 ) - the general solution is y ( t ) = 12 + C e − 4 t where C is a constant. Regardless of the value of the constant, lim t → ∞ y ( t ) = lim t → ∞ ( 12 + C e − 4 t ) = 12 (b) d y d t = 4 ( y − 12 ) - the general solution is y ( t ) = 12 + C e 4 t where C is a constant...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 10, Problem 33CRE

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The limit $\lim_{t \to \infty} y (t)$ if $y (t)$ is a solution of each of the given equations.

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Chapter 10, Problem 32CRE

Chapter 10, Problem 34CRE

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Chapter 10 Solutions

CALCULUS (CLOTH)

Ch. 10.1 - Prob. 1PQ Ch. 10.1 - Prob. 2PQ Ch. 10.1 - Prob. 3PQ Ch. 10.1 - Prob. 4PQ Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E

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The limit lim t → ∞ y ( t ) if y ( t ) is a solution of each of the given equations.

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The limit $\lim_{t \to \infty} y (t)$ if $y (t)$ is a solution of each of the given equations.

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Chapter 10 Solutions

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The limit $\lim_{t \to \infty} y (t)$ if $y (t)$ is a solution of each of the given equations.