Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.2 - Limits and Continuity - 14.2 Exercise: 28

Answer

Discontinuous for the unit circle $x^{2}+y^{2}=1$
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Work Step by Step

Use the maple command to plot the graph of the function as depicted below: From the above graph we observe a circular break in the graph, which corresponds to a unit circle for which the function is discontinuous. As the 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 the unit circle $x^{2}+y^{2}=1$
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