2. (Inspired by Alexander & Sadiku, Fundamentals of Electric Circuits, Ch. 15.) Use tables, not the integral (and not Maple!) to find Laplace transforms of the following signals. The trick here is that the tables are keyed off the $u(t)$ term and its time shift, so you need to re-write the signals with the same time shift in the main function as is in the unit step function. For instance, for $w(t) = 2tu(t - 4)$ (which you are not doing), you could write:
$w(t) = 2tu(t - 4)$
$= 2(t - 4 + 4)u(t - 4)$
$= 2(t - 4)u(t - 4) + 8u(t - 4)$
$W(s) = 2\frac{e^{-4s}}{s^2} + 8\frac{e^{-4s}}{s} = 2e^{-4s}\frac{1 + 4s}{s^2}$
• $x(t) = (t + 2)u(t - 3)$
• $y(t) = 2(t + 1)e^{-4t}u(t - 2)$
• $z(t) = 10\sin(3t - 1)u(t)$
