Signal Cutoff Gain (Electrical & Computer Engineering)

A digital signal processing (DSP) engineer is designing an ideal brick-wall low-pass filter. The normalized voltage gain $G(f)$ of the filter as a function of the signal frequency $f$ (in kHz) is modeled by:

At the cutoff frequency of $f = 4\text{ kHz}$, the filter's electronic circuitry experiences a singularity (direct evaluation yields $0/0$, making the exact gain value $G(4)$ undefined).

1. Explain why direct evaluation at $f = 4\text{ kHz}$ fails.
2. Use a numerical approach to show that as the input frequency approaches the cutoff $f = 4\text{ kHz}$ from the left ($f \to 4^-$) and right ($f \to 4^+$), the gain approaches a stable value. What is this limit?