Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 1 - Ingredients of Change: Functions and Limits - 1.3 Activities - Page 31: 33

Answer

a) $\lim\limits_{x \to -1^{-}}f(x)=1$ b) $\lim\limits_{x \to -1^{+}}f(x)=1$ c) $f(-1)=1$ d) It is continuous

Work Step by Step

a) Approaching $-1$ from the left side, we choose $x^{2}$; $\lim\limits_{x \to -1^{-}}f(x)$ $=$ $\lim\limits_{x \to -1^{-}}x^{2}=1$ b) Approaching $-1$ from the right side, we choose $1$; $\lim\limits_{x \to -1^{+}}f(x)$ $=$ $\lim\limits_{x \to -1^{+}}1=1$ c) Direct answer d) Since, $\lim\limits_{x \to -1^{-}}f(x)$ $=$ $\lim\limits_{x \to -1^{+}}f(x)$ $=$ $f(-1)=1$, It is continuous!
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