Answer
False
Work Step by Step
Since, it may be the case that , as ${ (x,y)\to (a,b)}$ along a curve ; not along a straight line through $(a,b)$.
Then, $\lim\limits_{ (x,y)\to (a,b)}f (x,y)\ne L$
Hence, the statement is false.
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 14 - Partial Derivatives - Review - True-False Quiz - Page 1022: 5
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