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: 3

Answer

$-2.5$

Work Step by Step

From table, we observe that the function $f(x,y)$ approaches to $-2.5$ ,as the $(x,y)$ approaches to $(0,0)$. Our guess can be proved by taking the help of substitution method as follows: $\lim\limits_{(x,y) \to(0,0)}f(x,y)=\lim\limits_{(x,y) \to(0,0)}f(x,y)\frac{x^{2}y^{3}+x^{3}y^{2}-5}{2-xy}$ $=\frac{-5}{2}=-2.5$
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