Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$
$$\mathop {Lt}\limits_{t \to \propto } \,\,f\left( t \right) = 1$$ then value of $$k$$ is

Let $$Y(s)$$ be the Laplace transform of function $$y(t),$$ then the final value of the function is __________.

The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.

The Laplace transform of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is __________.