Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - Review - Exercises - Page 1022: 10


Does not exist.

Work Step by Step

Along the line $x=0$, the value of limit is zero. Along $x=0$: $\lim\limits_{(x,y) \to (0,0)}\frac{2xy}{x^2+2y^2}=0$ Along $y=x$: $\frac{2x^2}{x^2+2x^2}=\frac{2}{3}$ Since along two different lines the limit has two different values, it does not exist.
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