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: 16

Answer

$0$

Work Step by Step

Given: $\lim\limits_{(x,y) \to (0,0)}f(x,y)=\frac{xy^{4}}{x^{4}+y^{4}}$ Divide both numerator and denominator by $y^{4}$. $=\lim\limits_{(x,y) \to (0,0)}\frac{x}{(\frac{x}{y})^{4}+1}$ $=\frac{\lim\limits_{(x,y) \to (0,0)}x}{\lim\limits_{(x,y) \to (0,0)}(\frac{x}{y})^{4}+1}$ $=\frac{0}{0+1}$ $=0$ Hence, the limit converges to $0$.
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.