Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 771: 3

$$10$$

Given $$\lim _{(x, y) \rightarrow(2,-1)}\left(x y-3 x^{2} y^{3}\right)$$ Since $ \left(x y-3 x^{2} y^{3}\right)$ is a continuous polynomial function, then by substitution, we get \begin{align*} \lim _{(x, y) \rightarrow(2,-1)}\left(x y-3 x^{2} y^{3}\right)&=\lim _{(x, y) \rightarrow(2,-1)}\left((2) (-1)-3 (2)^{2} (-1)^{3}\right)\\ &=-2+12=10 \end{align*}