Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises: 13

Answer

a) $\lim\limits_{x \to 0^-}$f(x)=1 b) $\lim\limits_{x \to 0^+}$f(x)=0 c) $\lim\limits_{x \to 0}$f(x) does not exist because $\lim\limits_{x \to 0^-}$f(x) $\ne$ $\lim\limits_{x \to 0^+}$f(x)=0

Work Step by Step

a) as x approaches 0 from the left-hand side, f(x) moves towards 1 b) as x approaches 0 from the right-hand side, f(x) moves towards 0 c) The limit does not exist because as x approaches 0 from both sides, for f(x) from the right side ≠ f(x) from the left side.
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