Thomas' Calculus 13th Edition

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

Chapter 14: Partial Derivatives - Section 14.2 - Limits and Continuity in Higher Dimensions - Exercises 14.2 - Page 796: 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) Take all the positive values for $\ln n$. Thus, for all (x,y,z) such that $z - x^2-y^2-1 \gt 0$ b) There can be no zero in the denominator.Therefore,for all $(x,y,z )$ such that $z \ne \sqrt {x^2+y^2}$
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