Question

3. If the Laplace transform of a function $f(t)$ is $F(s) = \frac{s}{s^2+4}$, then Laplace of $e^{-t}f(t)$.\\ A. $cos^2(t)$\ B. $\frac{s+1}{(s+1)^2+4}$\ C. $\frac{2}{(s+1)^2+4}$\ D. $\frac{s}{(s+1)^2(s+1)}$

          3. If the Laplace transform of a function $f(t)$ is $F(s) = \frac{s}{s^2+4}$, then Laplace of $e^{-t}f(t)$.\\
A. $cos^2(t)$\
B. $\frac{s+1}{(s+1)^2+4}$\
C. $\frac{2}{(s+1)^2+4}$\
D. $\frac{s}{(s+1)^2(s+1)}$

3. If the Laplace transform of a function f(t) is F(s) = (s)/(s^2+4), then Laplace of e^-tf(t).

A. cos^2(t)B. (s+1)/((s+1)^2+4)C. (2)/((s+1)^2+4)D. (s)/((s+1)^2(s+1))

Added by Jason S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Maria Dearborn

Step 1

We are given that the Laplace transform of f(t) is F(s) cos(ωt). The Laplace transform of cos(ωt) is given by: L{cos(ωt)} = s/(s^2 + ω^2) So, the Laplace transform of f(t) is F(s) times the Laplace transform of cos(ωt): L{f(t)} = F(s) * L{cos(ωt)} = Show more…

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