Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 772: 36

$$e^3$$

Given $$\lim _{(x, y) \rightarrow(2,1)} e^{x^{2}-y^{2}}$$ Since $ e^{x^{2}-y^{2}}$ is continuous at $(2,1)$, then by substitution, we get \begin{align*} \lim _{(x, y) \rightarrow(2,1)} e^{x^{2}-y^{2}}&=\lim _{(x, y) \rightarrow(2,1)} e^{4-1}\\ &=e^3 \end{align*}