Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 9



Work Step by Step

We will calculate the limit for $\lim\limits_{(x,y) \to (\pi,\ln 2)} e^y \cos x$ This implies that $\lim\limits_{(x,y) \to (\pi,\ln 2)} e^y \cos x=e^{(\ln 2)} \cos (\pi)$ Thus, $\lim\limits_{(x,y) \to (\pi,\ln 2)} e^y \cos x=e^{(\ln 2)} \cos (\pi)=2 \times (-1)=-2$
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