Question

Laplace Transforms Find the Laplace transform of each of the following. 1. f(t) = 6t^4 + 4e^15t - 3t^7/2 2. h(t) = 6cos(t/7) + 4cosh(7t) 3. g(t) = sin(2t) - 13e^-8t sin(2t) 4. h(t) = 4t sin(9t) + cos(1-7t)

          Laplace Transforms
Find the Laplace transform of each of the following.
1. f(t) = 6t^4 + 4e^15t - 3t^7/2
2. h(t) = 6cos(t/7) + 4cosh(7t)
3. g(t) = sin(2t) - 13e^-8t sin(2t)
4. h(t) = 4t sin(9t) + cos(1-7t)

Added by Charles W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/18/2023

Step 1

For f(t) = 6t' + 4e^(-5t) - 3t, we have: L{6t'} = 6L{t'} = 6\frac{1}{s^2} L{4e^(-5t)} = 4L{e^(-5t)} = 4\frac{1}{s+5} L{-3t} = -3L{t} = -3\frac{1}{s} So, the Laplace transform of f(t) is: L{f(t)} = \boxed{6\frac{1}{s^2} + 4\frac{1}{s+5} - 3\frac{1}{s}} Show more…

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Laplace Transforms Find the Laplace transform of each of the following: f(t) = 6t^4 + 4e^15t - 3t^7/2 h(t) = 6cos(t/7) + 4cosh(7t) g(t) = sin(2t) - 13e^-8t sin(2t) h(t) = 4t sin(9t) + cos(1-7t)