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: 39


a) For all $(x,y,z)$ such that $z \gt x^2+y^2+1$ b) For all $(x,y,z)$ such that $z \ne \sqrt {x^2+y^2}$

Work Step by Step

a) We can only take $\ln$ of positive values. Thus $z-x^2-y^2-1\gt 0$ b) There must not be zero in the denominator. So, for all $(x,y,z)$ such that $z \ne \sqrt {x^2+y^2}$
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