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: 38

Answer

a) For all (x,y,z) except the plane (x,0,0) that is, $x$-axis; b) For all $(x,y,z )$, except the plane (0,y,0) and (x,0,0), that is excluding x and y axes

Work Step by Step

a) There must not be zero in the denominator for that make sure $y\ne0$ and $ z \ne0$. Thus, all (x,y,z) except the plane (x,0,0). b) There must not be zero in the denominator for that make sure $x\ne0$ and $ z \ne0$.Thus, for all $(x,y,z )$, except the plane (0,y,0) and (x,0,0) and excluding x- and y- axes
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