Note: V0 is meant to indicate the voltage across the parallel branches in the schematic of the circuit.
When is the net reactance equal zero for the network comprised of the capacitor in parallel with the resistor/inductor combination?
Hint for 4.37
The net reactance for the network comprised of the capacitor in parallel with the resistor/inductor combination turns out to be purely resistive, 400 ohm.
Hint for 4.48
The effective impedance of the inductor in parallel with the capacitor is j XLXC (XC - XL).
Hint for 6.7
Take the output as the voltage across the parallel RC circuit.
The ratio of output to input voltage will be
Vo / Vs = (1 - w2/32 + jw/8)-1.
Find the resonant frequency; you may ignore the question about bandwidth...