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: 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 the 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 $0$.
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