Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises - Page 124: 5


$\lim\limits_{x \to 2^+}f(x) = f(2)$ $\lim\limits_{x \to 2^-}f(x) \neq f(2)$

Work Step by Step

$\lim\limits_{x \to 2^+}f(x) = f(2)$ As $x$ approaches $2$ from the right side, the value of the function approaches $f(2)$. Therefore, the function is continuous from the right. $\lim\limits_{x \to 2^-}f(x) \neq f(2)$ However, as $x$ approaches $2$ from the left side, the value of the function does not approach $f(2)$. Therefore, the function is discontinuous at $x=2$
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