Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 12



Work Step by Step

Consider $l=\lim\limits_{(x,y) \to (1,1)} \dfrac{x^3-y^3}{xy-1}$ and $l=\lim\limits_{(x,y) \to (1,1)} \dfrac{(x-y) [x^2 y^2+xy+1]}{(xy-1)}$ Hence, $l=\lim\limits_{(x,y) \to (1,1)} x^2y^2+xy+1=(1)^2(1)^2+1 \cdot 1+1=3$
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