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: 24



Work Step by Step

$\lim\limits_{(x,y) \to (2,2)}\dfrac{(x-y)}{(x^4-y^4)}=\lim\limits_{(x,y) \to (2,2)}\dfrac{(x-y)}{(x^2)^2-(y^2)^2}$ Thus, we get $\lim\limits_{(x,y) \to (2,2)}\dfrac{(x-y)}{(x-y)(x+y)(x^2+y^2)}=\lim\limits_{(x,y) \to (2,2)}\dfrac{1}{(x+y)(x^2+y^2)}$ Hence, $\dfrac{1}{(2+2)(4+4)}=\dfrac{1}{32}$
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