Chapter 15 - Differentiation in Several Variables - Chapter Review Exercises - Page 835: 9

$$6$$

Given $$ \lim _{(x, y) \rightarrow(1,-3)}\left(x y+y^{2}\right)$$ Since $ \left(x y+y^{2}\right) $ is a continuous function, then \begin{align*} \lim _{(x, y) \rightarrow(1,-3)}\left(x y+y^{2}\right)&=\lim _{(x, y) \rightarrow(1,-3)}\left((-3)+(-3)^{2}\right)\\ &=6 \end{align*}