41. The Laplace transform of $$i\left( t \right)$$ is given by $$I\left( s \right) = \frac{2}{{s\left( {1 + s} \right)}}.$$ As $$t \to \infty $$ the value of $$i\left( t \right)$$ tends to
42. The bilateral Laplace transform of $${e^{ - 1}}u\left( {t + 2} \right)$$ is
43. The bilateral Laplace transform of $${e^t}\cos 2tu\left( { - t} \right) + {e^{ - t}}u\left( t \right) + {e^{\frac{t}{2}}}u\left( t \right)$$ is
44. The bilateral Laplace transform of u(-t + 3) is
45. The Laplace transform of $$x\left( t \right)$$ is $$X\left( s \right) = {e^{ - 2s}}\frac{{6{s^2} + s}}{{{s^2} + 2s - 2}}$$
The initial value of $$x\left( t \right)$$ is
The initial value of $$x\left( t \right)$$ is
46. The bilateral Laplace transform of $${e^{\left( {3t + 6} \right)}}u\left( {t + 3} \right)$$ is
47. The Laplace transform of $$x\left( t \right)$$ is $$X\left( s \right) = \frac{{{e^{ - 3s}}\left( {2{s^2} + 1} \right)}}{{s\left( {s + 1} \right)\left( {s + 4} \right)}}$$
The final value of $$x\left( t \right)$$ is
The final value of $$x\left( t \right)$$ is
48. The Laplace transform of $$x\left( t \right)$$ is $$X\left( s \right) = \frac{{2{s^2} + 3}}{{{s^2} + 5s + 1}}$$
The initial value of $$x\left( t \right)$$ is
The initial value of $$x\left( t \right)$$ is