Engineering Mat...

The Laplace transform of \(\frac{{\left( {1 - {e^t}} \right)}}{t}\) is

Z-transform of (n ⋅ 3ⁿ) is

If the steady state value of f(t) is 0.5 and its Laplace transform is given by \(F\left( s \right) = \frac{b}{{s\left( {s + 1} \right)\left( {s + a} \right)}}\), where a > 0, then which of the following is true?

The Laplace transform of f(t) = t² e^-2t cos (3t) is,

If the Laplace transform of f(t) is given by \(F\left( s \right) = \frac{{3\left( {s + 3} \right)}}{{{s^2} + 65 + 8}}\), the value of f(0.5) is ______

Consider the differential equation \(\frac{{dy}}{{dt}} + ay = {e^{ - bt}}\) with the initial condition y(0) = 0. Then the Laplace transform Y(s) of the solution y(t) is

Find the Laplace transform of \(\mathop \smallint \limits_0^\infty \frac{{{e^{ - at}} - {e^{ - bt}}}}{t}dt\)

If z-transform of \({u_n} = \frac{{\left( {2{z^2} - 3z} \right)}}{{\left( {3{z^2} + 4} \right)}}\) ​then u_o is

The Fourier transform of \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{1 - \left| x \right|,\;\;\;\left| x \right| < 1}\\{0,\;\;\;\;\left| x \right| > 1}\end{array}} \right.\) is