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: 21

Answer

Since $~~\lim\limits_{x \to 0}f(x) \neq f(0)$, the function is not continuous at $x = 0$

Work Step by Step

$f(0) = 0$ $\lim\limits_{x \to 0^-}f(x) = cos(0)= 1$ $\lim\limits_{x \to 0^+}f(x) = 1-(0)^2= 1$ $\lim\limits_{x \to 0}f(x) = 1$ Note that $\lim\limits_{x \to 0}f(x) \neq f(0)$ Since $~~\lim\limits_{x \to 0}f(x) \neq f(0)$, the function is not continuous at $x = 0$
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