Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.2 Limits and Continuity - 14.2 Exercises - Page 951: 38


{$(x,y) | (x,y) \neq 0$}

Work Step by Step

From the given function $f(x,y)$ we can see that it represents a represents a rational function which is continuous on its domain $D$ except at $(0,0)$. Thus, the limit does not exist along the line $y=0$, when $(x,y)$ approaches to $0$ which cannot be the value of the function. Therefore, we can conclude that $f(x,y)$ is not continuous at $(0,0)$. This mean that $(x,y) \neq 0$ and $f(x,y)$ is discontinuous at $(0,0)$ Hence, {$(x,y) | (x,y) \neq 0$}
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