Find the Laplace transform of the following signals and their region of convergence:

(a) the reflection of the unit-step signal, i.e., u(−t). And then use the result together with the Laplace transform of u(t)to see if you can obtain the Laplace transform of a constant or x(t) = u(t) + u(−t) (assume u(0) = 0.5 so there is no discontinuity at t = 0).

(b) the non-causal signal y(t) = e^−|t|u(t + 1). Carefully plot it, and find its Laplace transform Y(s)by separating y(t)into a causal and a non-causal signals, y_c(t) and y_ac(t), and plot them separately. Find the ROC of Y(s),Y_c(s) and Y_ac(s).