Answer
$$\frac{\pi}{4} $$
Work Step by Step
Since the function $ \tan^{-1} (x^2- y)$ is continuous at $(2,3)$, then we have
$$ \lim\limits_{(x,y) \to (2,3)}\tan^{-1} (x^2- y)=\tan^{-1} (2^2- 3)=\frac{\pi}{4} .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 771: 6
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