Answer
$-\dfrac{\pi}{4}$
Work Step by Step
We need to find the limit for $\lim\limits_{(x,y,z) \to (1,-1,-1)} \tan^{-1} (x+y+z)$
or, $\tan^{-1} (1-1-1)=\tan^{-1} (-1)$
Thus, $-\tan^{-1} (\tan (\pi/4))=-\dfrac{\pi}{4}$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 13 - Practice Exercises - Page 749: 14
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