Program Explanation Given information: The three functions are as shown below. x 1 = t e − t x 2 = 10 n e − t sinh 10 − n t x 3 = 10 n e − t sin 10 − n t Time t is fix and greater than 0. Explanation: First calculate the limit of x 2 function for n tends to infinity as, lim n → ∞ x 2 ( t ) = lim n → ∞ ( 10 n e − t sinh 10 − n t ) lim n → ∞ x 2 ( t ) = lim n → ∞ ( t ( 10 n t ) e − t sinh ( 10 − n t ) ) lim n → ∞ x 2 ( t ) = lim h → 0 ( t h e − t sinh h ) lim n → ∞ x 2 ( t ) = t e − t lim h → 0 ( sinh h h ) Further, simplify the above equation as, lim n → ∞ x 2 ( t ) = t e − t lim h → 0 cosh ( 0 ) lim n → ∞ x 2 ( t ) = t e − t lim n → ∞ x 2 ( t ) = x 1 ( t ) Now, calculate the limit of x 3 function for n tends to infinity as,

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

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

Publisher: PEARSON

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 3.4, Problem 38P

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Program Description: Purpose of the problem is to show for each fixed t>0 , limn→∞x2(t)=limn→∞x3(t)=x1(t) where x1=te−t , x2=10ne−tsinh10−nt and x3=10ne−tsin10−nt .

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Chapter 3.4, Problem 37P

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Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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Program Description: Purpose of the problem is to show for each fixed t > 0 , lim n → ∞ x 2 ( t ) = lim n → ∞ x 3 ( t ) = x 1 ( t ) where x 1 = t e − t , x 2 = 10 n e − t sinh 10 − n t and x 3 = 10 n e − t sin 10 − n t .

Solution Summary: The author explains that the limit of x_2 function for n tends to infinity.

Concept explainers

Program Description: Purpose of the problem is to show for each fixed t>0 , limn→∞x2(t)=limn→∞x3(t)=x1(t) where x1=te−t , x2=10ne−tsinh10−nt and x3=10ne−tsin10−nt .

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Chapter 3 Solutions

Program Description: Purpose of the problem is to show for each fixed t &gt; 0 , lim n → ∞ x 2 ( t ) = lim n → ∞ x 3 ( t ) = x 1 ( t ) where x 1 = t e − t , x 2 = 10 n e − t sinh 10 − n t and x 3 = 10 n e − t sin 10 − n t .

Solution Summary: The author explains that the limit of x_2 function for n tends to infinity.

Concept explainers

Program Description: Purpose of the problem is to show for each fixed t>0 , limn→∞x2(t)=limn→∞x3(t)=x1(t) where x1=te−t , x2=10ne−tsinh10−nt and x3=10ne−tsin10−nt .

Want to see the full answer?

Chapter 3 Solutions

Program Description: Purpose of the problem is to show for each fixed t > 0 , lim n → ∞ x 2 ( t ) = lim n → ∞ x 3 ( t ) = x 1 ( t ) where x 1 = t e − t , x 2 = 10 n e − t sinh 10 − n t and x 3 = 10 n e − t sin 10 − n t .