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 $${e^{\left( {a + 2} \right)t + 5}}$$ exists?

The laplace transform of $$i(t)$$ is given by
$$I\left( s \right) = {2 \over {s\left( {1 + s} \right)}}$$ As $$t \to \infty ,$$ the value of $$i(t)$$ tends to __________.

If $$\,\,L\left\{ {f\left( t \right)} \right\} = F\left( s \right)$$ then $$\,\,\,L\left\{ {f\left( {t - T} \right)} \right\}$$ is equal to