Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 772: 27

$$-16e$$

Given $$\lim _{(z, w) \rightarrow(-2,1)} \frac{z^{4} \cos (\pi w)}{e^{z+w}} $$ Since $ \dfrac{z^{4} \cos (\pi w)}{e^{z+w}}$ is continuous every where, then by substitution, we get \begin{align*} \lim _{(z, w) \rightarrow(-2,1)} \frac{z^{4} \cos (\pi w)}{e^{z+w}}&=\lim _{(z, w) \rightarrow(-2,1)} \frac{(-2)^{4} \cos (\pi )}{e^{-1}}\\ &= -16e \end{align*}