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In Exercises 88-91, the Laplace transform of a function f is the function Lf (s) of the variable s defined by the improper integral (if it converges): Lf (s) = f (2) e™** dz Laplace transforms are widely used in physics and engineering. 88. Show that if f(x) = C where C is a constant, then f (s) = C/s for s> 0. 89. Show that if f(x) = sin az, then Lf (s) = a s² + a² 90. Compute f(s), where f(x) = ez and s> a.

In Exercises 88-91, the Laplace transform of a function f is the function Lf (s) of the variable s defined by the improper integral (if it converges): Lf (s) = f (2) e™** dz Laplace transforms are widely used in physics and engineering. 88. Show that if f(x) = C where C is a constant, then f (s) = C/s for s> 0. 89. Show that if f(x) = sin az, then Lf (s) = a s² + a² 90. Compute f(s), where f(x) = ez and s> a.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Exercises 88-91, the Laplace transform of a function f is the function Lf (s) of the variable s defined by the improper integral (if it converges): Lf(3) = f* f(z)e™** dz Laplace transforms are widely used in physics and engineering. 88. Show that if f(x) = C where C is a constant, then Lf (s) = C/s for s> 0. 89. Show that if f(x) = sin az, then Lf (s) = s² + a² 90. Compute f(s), where f(x) = eº and s> a. 91. Compute Lf(s), where f(z) = cos az and s> 0.
Transcribed Image Text:In Exercises 88-91, the Laplace transform of a function f is the function Lf (s) of the variable s defined by the improper integral (if it converges): Lf(3) = f* f(z)e™** dz Laplace transforms are widely used in physics and engineering. 88. Show that if f(x) = C where C is a constant, then Lf (s) = C/s for s> 0. 89. Show that if f(x) = sin az, then Lf (s) = s² + a² 90. Compute f(s), where f(x) = eº and s> a. 91. Compute Lf(s), where f(z) = cos az and s> 0.
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