University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.2 - Limits and Continuity in Higher Dimensions - Exercises - Page 691: 28


$\arctan (-\dfrac{\pi}{4})$

Work Step by Step

Solve $\lim\limits_{(x,y,z) \to (\frac{-1}{4},\frac{\pi}{2}, 2)} \tan^{-1} (xyz)$ Now, $\lim\limits_{(x,y,z) \to (\frac{-1}{4},\frac{\pi}{2}, 2)} \tan^{-1} (xyz)=\tan^{-1} [(\dfrac{-1}{4})(\dfrac{\pi}{2})(2)]$ Thus, we get $\tan^{-1}(-\dfrac{\pi}{4})=\arctan (-\dfrac{\pi}{4})$
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