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 797: 54


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Work Step by Step

When the function $f$ is continuous at $ (x_0,y_0)$ then $\lim\limits_{(x,y) \to (x_0,y_0) }f(x,y)=3$ This implies that the limit is equal to the function value and the function is continuous at that point. When the function $f$ is not continuous at $ (x_0,y_0)$ then the limit may or may not be equal to the function value, that is, $3$. It can be possible only when it is a removable discontinuity; in that case, the limit will not exist.
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