Problem 1. Obtain the Laplace or z transforms of the following time functions. a) f(t) = (0.5t + t)e-t. Note: Given X (s) = L(x(t)), fx(t)e-ate-st dt = fx(t)e-(s+a)dt = X(s+a). b) f(t) = f(t-T); {f(T) |0 T < T} is given. Note that f(t) is a periodic function with the period T. c) f(t) = d) f(k)= = eat 0 [1 0 for 0 < t < T for t > T for even k(k = 0, 2, 4, ...) for odd k(k = 1,3,5,...)