Given that $$L\left[ {f\left( t \right)} \right]\, = \,$$ $${{s + 2} \over {{s^2} + 1}},$$ $$$L\left[ {g\left( t \right)} \right] = {{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s + 2} \right)}},$$$ $$$h\left( t \right) = \int\limits_0^t {f\left( \tau \right)\,g\left( {t - \tau } \right)\,d\tau ,} $$$ $$L\left[ {h\left( t \right)} \right]$$ is

A system with an input x(t) and an output y(t) is described by the relation: y(t) = t x(t). This system is

The Fourier Transform of the signal $$x(t) = {e^{ - 3{t^2}}}$$ is of the following form, where A and B are constants:

A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero and the input is $${e^{3t}}$$, the output for $$t\, > \,0$$ is