Answer
No, see explanations.
Work Step by Step
Due to the gap at $a=0$, $\lim_{x\to0^−}k(x)≠\lim_{x\to0^+}k(x)$, we see that the limit $\lim_{x\to0}k(x)$ does not exist. Thus the discontinuity at $a=0$ can not be extended.
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 2: Limits and Continuity - Practice Exercises - Page 101: 36
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