Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

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



Work Step by Step

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*}
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