Calculus 8th Edition

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: 14

Answer

0

Work Step by Step

Given: $\lim\limits_{(x,y) \to (0,0)}f(x,y)=\frac{x^{3}-y^{3}}{ {x^{2}+xy+y^{2}}}$ Consider $f(x,y)=\frac{x^{3}-y^{3}}{ {x^{2}+xy+y^{2}}}=\frac{(x-y)(x^{2}+xy+y^{2})}{x^{2}+xy+y^{2}}$ $f(x,y)=(x-y)$ Put $x=0,y=0$ , we get $\lim\limits_{(x,y) \to (0,0)}f(x,y)=\lim\limits_{(x,y) \to (0,0)}(x-y)=0$ Hence,$\lim\limits_{(x,y) \to (0,0)}f(x,y)=\frac{x^{3}-y^{3}}{ {x^{2}+xy+y^{2}}}=0$
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