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 - Page 950: 16



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 $0$.
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