$4.$ A first$-$order RC circuit has a voltage source, a resistor of $0\mathrm{.}5$ k$,$ and a capacitor of $1\mathrm{.}592$F connected in series.

The output is the voltage across the capacitor.

$($a$)$ What type of filter is this?

$($b$)$ At what frequency in hertz does the frequency response have a magnitude of $0\mathrm{.}707($i$.$e$.,3$ dB$)?$ This is the

system$$s cutoff frequency.

$($c$)$ You can change the cutoff frequency by swapping out the resistor. What resistance would you use to achieve

a cutoff frequency of $2000$ Hz$?$ How does this change affect the impulse response?