The Heaviside function H is defined by H(t) = {0 t < 0 1 t ≥ 0 It is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on. (a) Sketch the graph of the Heaviside function. (b) Sketch the graph of voltage V(t) in a circuit if the switch is turned on at time t = 0 and 50 volts are applied instantaneously to the circuit. Write a formula for V(t) in terms of H(t). (c) Sketch the graph of voltage V(t) in a circuit if the switch is turned on at time t = 5 and 150 volts are applied instantaneously to the circuit and turned off at time t = 10. Write a formula for V(t) in terms of H(t).