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: 19

Answer

$\sqrt 3$

Work Step by Step

Given: $\lim\limits_{(x,y,z) ) \to (\pi,0,\frac{1}{3})} e^{y^{2}}tanxz$ Substitute $x=\pi,y=0,z=\frac{1}{3}$ $=\lim\limits_{(x,y,z) ) \to (\pi,0,\frac{1}{3})} e^{0^{2}}tan\frac{\pi}{3}$ $=1\times \sqrt 3$ $=\sqrt 3$ Hence, $\lim\limits_{(x,y,z) ) \to (\pi,0,\frac{1}{3})} e^{y^{2}}tanxz=\sqrt 3$
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