University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 13 - Practice Exercises - Page 749: 12



Work Step by Step

We need to find the limit for $\lim\limits_{(x,y) \to (1,1)} \dfrac{x^3-y^3}{xy-1}$ or, $\lim\limits_{(x,y) \to (1,1)} \dfrac{(x-y) [(xy)^2+xy+1]}{(xy-1)}=\lim\limits_{(x,y) \to (1,1)} x^2+xy+1$ Thus, $1+(1)(1)+1=3$
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