Transform Theory - Study Mode
[#31] The Laplace transform of $$ileft( t
ight)$$ xa0is given by $$Ileft( s
ight) = frac{2}{{sleft( {1 + s}
ight)}}.$$ xa0 xa0As $$t o infty $$ xa0the value of $$ileft( t
ight)$$ xa0tends to
Correct Answer
(C) 2
[#32] The bilateral Laplace transform of $${e^{ - 1}}uleft( {t + 2}
ight)$$ xa0 is
Correct Answer
(A) $$frac{{{e^{2left( {s + 1}
ight)}}}}{{s + 1}},,,,,operatorname{Re} left( s
ight) > - 1$$
[#33] The bilateral Laplace transform of $${e^t}cos 2tuleft( { - t}
ight) + {e^{ - t}}uleft( t
ight) + {e^{frac{t}{2}}}uleft( t
ight)$$ xa0 xa0xa0 is
Correct Answer
(A) $$frac{{1 - s}}{{{{left( {s - 1}
ight)}^2} + 4}} + frac{1}{{s + 1}} + frac{1}{{s - 0.5}},,0.5 < operatorname{Re} left( s
ight) < 1$$
[#34] The bilateral Laplace transform of u(-t + 3) is
Correct Answer
(B) $$frac{{ - {e^{ - 3s}}}}{s},,,,,,operatorname{Re} left( s
ight) < 0$$
[#35] The Laplace transform of $$xleft( t
ight)$$ xa0is $$Xleft( s
ight) = {e^{ - 2s}}frac{{6{s^2} + s}}{{{s^2} + 2s - 2}}$$ The initial value of $$xleft( t
ight)$$ xa0is
Correct Answer
(D) 0