Answer
$0$
Work Step by Step
$\lim\limits_{(x,y) \to (0,0)}\frac{x^4-y^4}{x^2+y^2}=\lim\limits_{(x,y) \to (0,0)}\frac{(x^2+y^2)(x^2-y^2)}{x^2+y^2}=\lim\limits_{(x,y) \to (0,0)}x^2-y^2=0^2-0^2=0$
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 14 - Partial Derivatives - 14.2 Exercises - Page 923: 14
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