## Calculus (3rd Edition)

$$\frac{\pi}{4}$$
Since the function $\tan^{-1} (x^2- y)$ is continuous at $(2,3)$, then we have $$\lim\limits_{(x,y) \to (2,3)}\tan^{-1} (x^2- y)=\tan^{-1} (2^2- 3)=\frac{\pi}{4} .$$