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: 28


Discontinuous for unit circle $x^{2}+y^{2}=1$

Work Step by Step

Use maple command to plot the graph of the function as depicted below: From the above graph we observe that a circular break in the graph, which corresponds to unit circle for which function is discontinuous. As function $f(x,y)=\frac{1}{1-x^{2}-y^{2}}$ is a rational function, it is continuous except where $1-x^{2}-y^{2}=0$ or $x^{2}+y^{2}=1$ Therefore,the function $f(x,y)=\frac{1}{1-x^{2}-y^{2}}$ is discontinuous for unit circle $x^{2}+y^{2}=1$
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