Answer
$3$
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, $1+(1)(1)+1=3$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 13 - Practice Exercises - Page 749: 12
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