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: 27

Answer

Discontinuous along the line $y=x$
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Work Step by Step

Consider the function $f(x,y)=e^{1/x-y}$ Use the maple command to plot the graph of the function as depicted below: Suppose $x-y=0$ $y=x$ Therefore, the function $f(x,y)=e^{1/x-y}$is discontinuous at all points which satisfy $y=x$ Hence, the function is discontinuous along the line $y=x$
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