Explanation Given: The given statement is, “ L { ∫ 0 t e a τ f ( τ ) d τ } = _ whereas L { e a t ∫ 0 t f ( τ ) d τ } = _ . ” Formula used: If the Laplace transform of L { f ( t ) } = F ( s ) and a > 0 , then property of the Laplace transform is expressed as follows, L { ∫ 0 t f ( t ) d t } = F ( s ) s If the Laplace transform of L { f ( t ) } = F ( s ) then, L { e a t f ( t ) } = F ( s − a ) Calculation: From the above definition the Laplace transform of the given function is expressed as, L

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4, Problem 24CR

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To fill: The blank in the statement “L{∫0teaτf(τ)dτ}= _ whereas L{eat∫0tf(τ)dτ}= _.”.

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Chapter 4, Problem 23CR

Chapter 4, Problem 25CR

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2. Consider the following statement: For each natural number n, (3.2n+2.3n+1) is a prime number. (a) Explore this statement by completing the table below for n = 2,3 and two additional values of n of your choosing (notice n = 1 has been completed for you). One of your rows should contain a counterexample. n 1 3.2 2.3 +1 3.212.31 + 1 = 13 prime or composite? prime 2 3 (b) Write a formal counterexample argument for the statement using the template from

Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.

Chapter 4 Solutions

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The blank in the statement “ L { ∫ 0 t e a τ f ( τ ) d τ } = _ whereas L { e a t ∫ 0 t f ( τ ) d τ } = _ . ”.

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To fill: The blank in the statement “L{∫0teaτf(τ)dτ}= _ whereas L{eat∫0tf(τ)dτ}= _.”.

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Chapter 4 Solutions