Explanation Given: The given expression for function is f ( t ) = 1 t 2 . Concept used: If f ( t ) is a piecewise continuous function and is exponential of order t > 0 then the Laplace transform of f ( t ) is expressed as L ( f ( t ) ) = ∫ 0 ∞ e − s t f ( t ) d t . If L ( f ( t ) ) =I 1 + I 2 , and if I 1 diverges then, f ( t ) does not possess a Laplace solution. Calculation: Use the definition above to write the Laplace transform of the given function. L ( f ( t ) ) = ∫ 0 ∞ e − s t t 2 d t = ∫ 0 1 e − s t t 2 d t + ∫ 1 ∞ e − s t t 2 d t = I 1 + I 2 Use comparison test in three cases: s > 0 , s = 0 , and s < 0 . Consider s > 0

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.1, Problem 53E

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Chapter 4.1, Problem 52E

Chapter 4.1, Problem 54E

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Chapter 4 Solutions

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The given function does not possess a Laplace transform.

Solution Summary: The author explains that f(t) does not possess a Laplace transform.

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Chapter 4 Solutions