The Laplace Transform of e_at .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to

The final value theorem is used to find the

If L$$\left[ {f\left( t \right)} \right]$$ = $${{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$, then $$f\left( {0 + } \right)\,$$ and $$f\left( \infty \right)$$ are given by

The laplace transform of a unit ramp function starting at t=a, is