Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 772: 33

$$ e^{4} \ln (4)$$

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