University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.2 - Limits and Continuity in Higher Dimensions - Exercises - Page 691: 22



Work Step by Step

Consider $P(x,y)=xy$ and the point $P(x,y) \to O(0,0)$ This means that $xy \to 0$ Plug in: $u=xy$ Now, $\lim\limits_{u \to 0}\dfrac{1-\cos u}{u}=\dfrac{0}{0}$, which shows the limit of Indeterminate form; thus, we will apply L-Hospital's rule: We get $\lim\limits_{u \to 0}\dfrac{\sin u}{(1)}=\sin (0)=0$
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