Chapter 15 - Differentiation in Several Variables - Chapter Review Exercises - Page 835: 13

$$-e^{-4}$$

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