Thomas' Calculus 13th Edition

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: 35

Answer

No, see explanations.
1575133592

Work Step by Step

See graph. Due to the gap at $a=0$, $lim_{t\to0^-}h(t)\ne lim_{t\to0^+}h(t)$ and the limit $lim_{t\to0}h(t)$ does not exist. Thus the discontinuity at $a=0$ can not be extended.
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