Figure $2$: Circuit for Problem $2.$

Problem $2$: Concept$-10\%$

In this problem we will analyze the the circuit shown in Figure $2$ by exploring the behavior at extreme frequencies. As we will see, the circuit is a filter.

a$)$ Redraw the circuit for very low frequencies, $$~~$0.$

b$)$ What is the output voltage, $V_{\text{o}\text{u}\text{t}},$ in this case?

c$)$ Redraw the circuit for very high frequencies, $$~~$.$

d$)$ What is the output voltage, $V_{\text{o}\text{u}\text{t}},$ in this case?

e$)$ What is the cutoff frequency of the filter? Hint: ${}_c=\frac{1}{}.$

f$)$ What kind of filter is the circuit?