Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises - Page 92: 5


a) $\lim\limits_{x \to 1}f(x) = 2$ b) $\lim\limits_{x \to 3^-}f(x) = 1$ c) $\lim\limits_{x \to 3^+}f(x) = 4$ d) limit does not exist e) $f(3) = 3$

Work Step by Step

a) As $x$ approaches $1$ from both sides, $f(x)$ approaches 2. b) As $x$ approaches $3$ from the left hand side, $f(x)$ approaches $1$.. c) As $x$ approaches $3$ from the right hand side, $f(x)$ approaches $4$ d) Since the left and right hand limits (from parts b and c respectively) are not equal, the limit of $f(x)$ as $x$ approaches $3$ does not exist. e) The value of $f(x)$ at $x = 3$ is $3$ as indicated by the solid dot on the graph.
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