If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {K \over {\left( {s + 1} \right)\,\left( {{s^2} + 4} \right)}}$$ then $$\matrix{ {Lim\,f\,\left( t \right)} \cr {t \to \infty } \cr } $$ is given by

The Laplace transform of a function f(t)u(t), where f(t) is periodic with period T, is A(s) times the Laplace transform of its first period. Then

Laplace transform of the functions t u(t) and u(t) sin(t) are respectively: