Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}\,\,\,\,\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0$$

The final value of f(t) would be:

In what range should Re(s) remain so that the Laplace transform of the function e^(a+2)t+5 exists?

The Laplace transform of a continuous - time signal x(t) is $$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If the Fourier transform of tyhis signal exists, then x(t) is

The inverse Laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is