Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 772: 35

$$-48$$

Given $$\lim _{(x, y) \rightarrow(-3,-2)}\left(x^{2} y^{3}+4 x y\right)$$ Since $ \left(x^{2} y^{3}+4 x y\right)$, then by substitution, we get \begin{align*} \lim _{(x, y) \rightarrow(-3,-2)}\left(x^{2} y^{3}+4 x y\right)&=\lim _{(x, y) \rightarrow(-3,-2)}\left((-3)^{2} (-2)^{3}+4 (-3)(-2)\right)\\ &= -48 \end{align*}