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: 35


a) for all (x,y,z) b) For all (x,y) except the interior of the cylinder $x^2+y^2=1$

Work Step by Step

a) As we can see that there are no square roots and fractions , therefore, all values are possible , that is, for all $(x,y,z)$ b) There must be possibility that in the xy plane $x^2+y^2-1 \geq 0$ so, $x^2+y^2 \geq 1$. In order to make sure that the radical does not contain any negative value.
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