Chapter 14: Partial Derivatives - Section 14.2 - Limits and Continuity in Higher Dimensions - Exercises 14.2 - Page 797: 55

Yes

Given : $1 - \dfrac{x^2 y^2}{3} \lt \dfrac{\tan^{-1} (xy)}{xy} \lt 1$ Since, $\lim\limits_{(x,y) \to (0,0) } (1 - \dfrac{x^2 y^2}{3})=1$ and $\lim\limits_{(x,y) \to (0,0) } 1=1$ This implies that the limit for $\lim\limits_{(x,y) \to (0,0) } (\dfrac{\tan^{-1} (xy)}{xy} )=1$ by the Sandwich Theorem. So, our answer is Yes.