Question

1. Find the Laplace transform of the following functions. (a) f(t)=sin(2t)cos(2t) (b) f(t)=cos²(3t) (c) f(t)=t e²? sin(3t) 2- Find the Laplace transforms of the given functions. (a) f(t) = 6e??? + e³? + 5t³ - 9 (b) g(t) = 4 cos(4t) - 9 sin(4t) + 2 cos(10t) (c) h(t) = 3 sinh(2t) + 3 sin(2t) (d) g(t) = e³? + cos(6t) - e³? cos(6t) 3. Find the transform of each of the following functions. (a) f(t) = t cosh(3t) (b) h(t) = t² sin(2t)

          1. Find the Laplace transform of the following functions.
(a) f(t)=sin(2t)cos(2t)
(b) f(t)=cos²(3t)
(c) f(t)=t e²? sin(3t)
2- Find the Laplace transforms of the given functions.
(a) f(t) = 6e??? + e³? + 5t³ - 9
(b) g(t) = 4 cos(4t) - 9 sin(4t) + 2 cos(10t)
(c) h(t) = 3 sinh(2t) + 3 sin(2t)
(d) g(t) = e³? + cos(6t) - e³? cos(6t)
3. Find the transform of each of the following functions.
(a) f(t) = t cosh(3t)
(b) h(t) = t² sin(2t)

1. Find the Laplace transform of the following functions.
(a) f(t)=sin(2t)cos(2t)
(b) f(t)=cos²(3t)
(c) f(t)=t e²? sin(3t)
2- Find the Laplace transforms of the given functions.
(a) f(t) = 6e??? + e³? + 5t³ - 9
(b) g(t) = 4 cos(4t) - 9 sin(4t) + 2 cos(10t)
(c) h(t) = 3 sinh(2t) + 3 sin(2t)
(d) g(t) = e³? + cos(6t) - e³? cos(6t)
3. Find the transform of each of the following functions.
(a) f(t) = t cosh(3t)
(b) h(t) = t² sin(2t)

Added by Jaime B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Arjun Singh

01/04/2022

Step 1

(a) The Laplace transform of f(t) = zsin(2t)cos(2t) can be simplified using the double-angle identity sin(2x) = 2sin(x)cos(x). So, f(t) = zsin(2t)cos(2t) = z/2sin(4t). The Laplace transform of sin(at) is a/(s^2 + a^2). Therefore, the Laplace transform of f(t) is Show more…

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1. Find the Laplace transform of the following functions. (a) f(t) = sin(2t)cos(2t) (b) f(t) = cos^2(3t) (c) f(t) = t e^{2t} sin(3t) 2- Find the Laplace transforms of the given functions. (a) f(t) = 6e^{-5t} + e^{3t} + 5t^3 - 9 (b) g(t) = 4 cos(4t) - 9 sin(4t) + 2 cos(10t) (c) h(t) = 3 sinh(2t) + 3 sin(2t) (d) g(t) = e^{3t} + cos(6t) - e^{3t} cos(6t) 3. Find the transform of each of the following functions. (a) f(t) = t cosh(3t) (b) h(t) = t^2 sin(2t)