Explanation Given: The given statement is, ‘If f is not piecewise continuous on [ 0 , ∞ ) , then L { f ( t ) } will not exist.’ Formula used: A piecewise function is continuous on a given interval if the following conditions are satisfied. 1) Its constituent function is continuous on the corresponding interval. 2) There is no discontinuity at the end of sub domain within the interval. Laplace transform of the function is as follows, L { t α } = ( α + 1 ) s α + 1 where α > − 1 . From the property of the gamma function, Γ ( 1 2 ) = π Calculation: From the above statement assume a function which is not piecewise continuous in the given interval [ 0 , ∞ )

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Solution Summary: The author explains that if f is not piecewise continuous, then it will not exist. The Laplace transform of the function is expressed as follows.

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