Question

1. Find the Laplace transform of each of the following: a) f(t) = {0, t < 2; 2t, t ? 2 b) f(t) = {sin t, t < 4??; cost, t ? 4?? c) f(t) = e^2t sin 2t 2. Find the inverse Laplace transform of each of the following: a) 2 / (s - 2)^4 b) (s - 3) / ((s - 2)^2 + 16) c) (4e^-2??s) / (s^2 + 1) d) e^-2s / (s^2 + 3s)

          1. Find the Laplace transform of each of the following:
a) f(t) = {0, t < 2; 2t, t ? 2
b) f(t) = {sin t, t < 4??; cost, t ? 4??
c) f(t) = e^2t sin 2t
2. Find the inverse Laplace transform of each of the following:
a) 2 / (s - 2)^4
b) (s - 3) / ((s - 2)^2 + 16)
c) (4e^-2??s) / (s^2 + 1)
d) e^-2s / (s^2 + 3s)

1. Find the Laplace transform of each of the following:
a) f(t) = 0, t < 2; 2t, t ? 2
b) f(t) = sin t, t < 4??; cost, t ? 4??
c) f(t) = e^2t sin 2t
2. Find the inverse Laplace transform of each of the following:
a) 2 / (s - 2)^4
b) (s - 3) / ((s - 2)^2 + 16)
c) (4e^-2??s) / (s^2 + 1)
d) e^-2s / (s^2 + 3s)

Added by Mario N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/03/2023

Step 1

Find the Laplace transform of each of the following: a) f(t) = 12t Using the Laplace transform formula, we have: $$\mathcal{L}\{12t\} = \int_0^\infty 12t e^{-st} dt$$ To solve this integral, we can use integration by parts: Let u = 12t, dv = e^{-st} dt Then, Show more…

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Find the Laplace transform of each of the following: (a) f(t) = 12t, t < 2 (b) f(t) = cost, t < 41 (c) f(t) = e^2t sin 2t 2. Find the inverse Laplace transform of each of the following: (a) 5 - 3/(6s - 27 + 16) (b) 4e^(-2n) / (s^2 + 52s + 1) (c) 5t^3