University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.2 - Limits and Continuity in Higher Dimensions - Exercises - Page 691: 34


a) For all (x,y) except the lines $x=2$ and $x=1$ b) For all (x,y) except parabola $y=x^2$

Work Step by Step

a) There must not be zero in the denominator. After factoring the denominator into $(x-2)(x-1)$, we see that the function is defined for all $(x,y)$ except the lines $x=2$ and $x=1$ b) To avoid the denominator being zero, we make sure that $x^2-y\ne 0$ or $y\ne x^2$.
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