Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.2 - Limits and Continuity in Higher Dimensions - Exercises 14.2 - Page 796: 9



Work Step by Step

Here, $\lim\limits_{(x,y) \to (0,0)} e^y(\dfrac{\sin x}{x})=e^{0} \lim\limits_{(x \to0)} (\dfrac{\sin x}{x})$ Then, we have $\lim\limits_{(x,y) \to (0,0)} e^y(\dfrac{\sin x}{x})=(1)(1)=1$
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