Where the transfer functions of the controller and plant are given byhc(s) =s+ 1sandhp(s) =1s+ 2respectively. letx(t) =au(t) for parts () below.(a) show that limt→[infinity]y(t) =a.(b) determine the error signale(t) =x(t)−y() does the system track the input signal (i. e., does limt→[infinity]e(t) = 0) if the transferfunction, hc(s), of the controller is changed tohc(s) =1s−2? justify your answer.