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: 37


a) For all $(x,y,z)$ except the plane where $z=0$ b) For all $(x,y,z)$ excluding the surface of the cylinder $x^2+z^2=1$

Work Step by Step

a) We know that $\sin t$ is defined for all real numbers. Since we can not have a zero in the denominator $z \ne 0$. b) We can not have a zero in the denominator, thus: $x^2+z^2-1\ne 0$. Thus we must exclude the surface of the cylinder $x^2+z^2=1$.
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