1
GATE ECE 2009
+2
-0.6
Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)\,d\tau }$$ is
A
$$sF\left( s \right) - f\left( 0 \right)$$
B
$$\,{1 \over s}F\left( s \right)\,$$
C
$$\int\limits_0^s {F\left( \tau \right)d\tau }$$
D
$${1 \over s}\left[ {F\left( s \right) - f\left( 0 \right)} \right]$$
2
GATE ECE 2006
+2
-0.6
Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}\,\,\,\,\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0$$

The final value of f(t) would be:

A
0
B
1
C
$$- e\,\,\, - 1 \le f\left( \infty \right) \le 1$$
D
$$\infty$$
3
GATE ECE 2005
+2
-0.6
In what range should Re(s) remain so that the Laplace transform of the function e(a+2)t+5 exists?
A
Re(s) > a+2
B
Re(s) > a+7
C
Re(s) < 2
D
Re(s) > a+5
4
GATE ECE 2002
+2
-0.6
The Laplace transform of a continuous - time signal x(t) is $$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If the Fourier transform of tyhis signal exists, then x(t) is
A
$${e^{2t}}u\left( t \right) - 2\,{e^{ - t}}u\left( t \right)$$
B
$$- {e^{2t}}u\left( { - t} \right) + 2\,{e^{ - t}}u\left( t \right)$$
C
$$- {e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$
D
$${e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$
EXAM MAP
Medical
NEET