Answer
$2$
Work Step by Step
Here, we have $\lim\limits_{(x,y) \to (0,0)} \dfrac{(\sqrt x-\sqrt y)(\sqrt x+\sqrt y+2)}{\sqrt x-\sqrt y}=\lim\limits_{(x,y) \to (0,0)} (\sqrt x+\sqrt y+2)$
Plug the limits, then we get $(0+0+2)=2$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 14: Partial Derivatives - Section 14.2 - Limits and Continuity in Higher Dimensions - Exercises 14.2 - Page 796: 17
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