Transform Theory - Study Mode
[#41] The Laplace transform F(s) of the exponential function. f(t) = e at when t ≥ 0, where a is a constant and (s - a) > 0, is
Correct Answer
(B) $$frac{1}{{{ ext{s}} - { ext{a}}}}$$
[#42] Evaluate $$intlimits_0^infty {frac{{sin { ext{t}}}}{{ ext{t}}}{ ext{dt}}} $$
Correct Answer
(B) $$frac{pi }{2}$$
[#43] If the Laplace transform of $${{ ext{e}}^{omega { ext{t}}}}$$ xa0is $$frac{1}{{{ ext{s}} - omega }},$$ xa0the Laplace transform of tcosh t is
Correct Answer
(A) $$frac{{1 + {{ ext{s}}^2}}}{{{{left( {{{ ext{s}}^2} - 1}
ight)}^2}}}$$
[#44] The function f(t) satisfies the differential equation $$frac{{{{ ext{d}}^2}{ ext{f}}}}{{{ ext{d}}{{ ext{t}}^2}}} + { ext{f}} = 0$$ xa0 and the auxiliary conditions, f(0) = 0, $$frac{{{ ext{df}}}}{{{ ext{dt}}}}left( 0
ight) = 4.$$ xa0The Laplace transform of f(t) is given by
Correct Answer
(C) $$frac{4}{{{{ ext{s}}^2} + 1}}$$
[#45] The Laplace transform of e i5t where $${ ext{i}} = sqrt { - 1} ,$$ xa0 is
Correct Answer
(B) $$frac{{{ ext{s}} + 5{ ext{i}}}}{{{{ ext{s}}^2} + 25}}$$