Answer
$-2/3$
Work Step by Step
Factoring out $x+y$
$$\lim\limits_{(x,y) \to (2,-1)} \frac{xy(x+y)}{(x+y)(x-y)}= \lim\limits_{(x,y) \to (2,-1)} \frac{xy}{(x-y)} = \frac{2*-1}{2+1}=-2/3$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 14 - Partial Derivatives - 14.2 Limits and Continuity - 14.2 Exercises - Page 950: 6
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