Flow Control Valve Restriction (Civil & Environmental Engineering)

A water resources engineer designs an automated municipal overflow valve for a storm runoff conduit. The flow discharge velocity factor $V(x)$ (in $\text{m/s}$) through the throttle orifice is modeled as a function of the aperture opening width $x$ (in centimeters) by:

During valve tuning, the aperture is calibrated around the critical transition setting $x = 3\text{ cm}$.

1. Explain why direct evaluation at $x = 3\text{ cm}$ fails.
2. Apply an algebraic factoring strategy to find the limiting flow velocity $\lim_{x\to 3} V(x)$.