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

If $$\,\,\,L\,\,\left\{ {f\left( t \right)} \right\} = {w \over {{s^2} + {w^2}}}$$ then the value of
$$\mathop {Lim}\limits_{t \to \infty } f\left( t \right) = $$ ____________.

The laplace transform of $${e^{\alpha t}}\,\cos \,\alpha \,t$$ is equal to ____________.