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Find the Laplace transform F(s) = L{f(t)} of each of the following functions. (i) f(t) = t^2 / 3 ( e^4t + e^−4t ) Hint – Use the Linearity Property and the Table of Laplace Transforms. (ii) f(t) = e^3t ( sin(t) + cos(t)) Hint – Use the Linearity Property and the Table of Laplace Transforms. (iii) f(t) = t( sin (2t) + cos (2t)) Hint – Use the Transform Derivative Principle and the Table of Laplace Transforms.

Find the Laplace transform F(s) = L{f(t)} of each of the following functions. (i) f(t) = t^2 / 3 ( e^4t + e^−4t ) Hint – Use the Linearity Property and the Table of Laplace Transforms. (ii) f(t) = e^3t ( sin(t) + cos(t)) Hint – Use the Linearity Property and the Table of Laplace Transforms. (iii) f(t) = t( sin (2t) + cos (2t)) Hint – Use the Transform Derivative Principle and the Table of Laplace Transforms.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Find the Laplace transform

F(s) = L{f(t)} of each of the following functions.

(i) f(t) = t^2 / 3 ( e^4t + e^−4t )

Hint – Use the Linearity Property and the Table of Laplace Transforms.

(ii) f(t) = e^3t ( sin(t) + cos(t))

Hint – Use the Linearity Property and the Table of Laplace Transforms.

(iii) f(t) = t( sin (2t) + cos (2t))

Hint – Use the Transform Derivative Principle and the Table of Laplace Transforms.

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