Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.2 - Limits and Continuity - 14.2 Exercise: 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,$\lim\limits_{(x,y) \to (0,0)}f(x,y)=\frac{x^{3}-y^{3}}{ {x^{2}+xy+y^{2}}}=0$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.