Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.1 Exercises - Page 105: 96



Work Step by Step

This statement is true because, by definition, a function can only be differentiable at a point $k$ if, and only if, the function is continuous at $k$ and $\lim\limits_{x \to k^{-}} f(x) = \lim\limits_{x \to k^{+}} f(x)$. Therefore, if a function is differentiable at a point, it is guaranteed to be continuous at that point.
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