(a) Program Explanation Given information: Transforms of derivatives theorem loosely states that L { f ′ ( t ) } = s L { f ( t ) } − f ( 0 ) for the function f ( t ) that is piecewise continuous. Calculation: Consider f ( t ) as 1 t n e a t and apply the derivative transform theorem as, L { f ′ ( t ) } = s L { f ( t ) } − f ( 0 ) L { ( t n e a t ) ′ } = s L { t n e a t } − ( ( 0 ) n e a ( 0 ) ) L { n t n − 1 e a t + a t n e a t } = s L { t n e a t } − 0 n L { t n < (b) Program Plan Intro Program Description: Purpose of the problem is to deduce L { t n e a t } = n ! ( s − a ) n + 1 for n as natural number.

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Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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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 7.2, Problem 27P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that L{tneat}=ns−aL{tn−1eat}

(b)

Program Plan Intro

Program Description: Purpose of the problem is to deduce L{tneat}=n!( s−a)n+1 for n as natural number.

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Chapter 7.2, Problem 26P

Chapter 7.2, Problem 28P

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Chapter 7 Solutions

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Program Description: Purpose of the problem is to show that L { t n e a t } = n s − a L { t n − 1 e a t }

Solution Summary: The author explains the purpose of the problem, which is to show that Llefttneatright=

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Program Description: Purpose of the problem is to show that L{tneat}=ns−aL{tn−1eat}

Program Description: Purpose of the problem is to deduce L{tneat}=n!( s−a)n+1 for n as natural number.

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Chapter 7 Solutions