Answer
False
Work Step by Step
Counterexample
\[
f(x, y)=\frac{yx}{y^{2}+x^{2}}
\]
Has limit $0=x$
Has limit $0=y$
but if $k \neq 0,$ along the line $k x=y$, it is not zero.
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 13 - Partial Derivatives - 13.2 Limits And Continuity - Exercises Set 13.2 - Page 926: 30
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