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: 33


a) for all (x,y) except the $x$-axis (y=0) and the y-axis (x=0) b) for all (x,y)

Work Step by Step

a) We know that $\sin t$ is defined for all real numbers. Thus, for all $(x,y)$ and there must not be zero in the denominator. Thus, for all $(x,y)$ except $y=x=0$ b) The minimal value for $\cos x$ is $-1$. Thus the denominator will never be zero. Hence, all real numbers.
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