Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2: 31

Answer

(a) $\lim\limits_{x \to 3^{-}}f(x)$ = 2 (b) $\lim\limits_{x \to 3^{+}}f(x)$ = 2 (c) $\lim\limits_{x \to 3}f(x)$ = 2

Work Step by Step

(a) In this case x $\leq$ 3, then $f(x)$ = x - 1. $\lim\limits_{x \to 3^{-}}f(x)$ = $\lim\limits_{x \to 3^{-}}x-1$ = 3 - 1 = 2 (b) In this case x $\gt$ 3, then $f(x)$ = 3x - 7 $\lim\limits_{x \to 3^{+}}f(x)$ = $\lim\limits_{x \to 3^{+}}3x-7$ = 3$\times$3 - 7 = 2 (c) As $\lim\limits_{x \to 3^{+}}f(x)$ = $\lim\limits_{x \to 3^{-}}f(x)$ = 2, we conclude that $\lim\limits_{x \to 3}f(x)$ = 2
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