For a stirred-tank heater, assume the transfer function between the heater input change u(t) (cal/sec) and the tank temperature change y(t)(^∘C) can be modeled as G(s) = 5 / 3s + 1 

(a) Using the Final Value Theorem, find the steady-state response for a unit rectangular pulse change in the heating rate (U(s) = 1 - e^-s / s).

(b) Repeat the calculation in (a) for a unit ramp (U(s) = 1 / s²).

(c) For both cases (a) and (b), explain your answer physically. Is there a physical limitation on the ramping of the heating rate?