Find f (t) for each of the following functions. Also apply the initial- and final-value theorems. (a) F(s) = s + 1/s(s^2 + 4s + 4). (b) F(s) = s – 10/(s^4 + s^2). (c) F(s) = s + 8/s^2(s^2 + 4s + 4) (d) F(s) = 1/s(s + 1) – e^-s/s(s + 1). Find f (t) for each of the following functions. Also apply the initial- and final-value theorems where possible. If not possible, explain. (a) F(s) = 8s^2 + 37s + 32/(s + 1)(s + 2)(s + 4). (b) = F(s) = 250(s + 7)(s + 14)/s(s^2 + 14s + 50). (c) F(s) = 5(s + 2)^2/s(s + 1)^3 (d) F(s) = 400/s(s^2 + 4s + 5)^2.
