Answer
$-(\dfrac{\pi}{4})$
Work Step by Step
Consider $l=\lim\limits_{(x,y,z) \to (1,-1,-1)} \tan^{-1} (x+y+z)$
and $l=\tan^{-1} (1-1-1)=\tan^{-1} (-1)$
Hence, $l=-\tan^{-1} (\tan (\dfrac{\pi}{4}))=-(\dfrac{\pi}{4})$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 14
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