Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.2 - Finding Limits Using Properties of Limits - Exercise Set - Page 1153: 44


a) $7$ b) $10$ c) Limit does not exist.

Work Step by Step

Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$. In order to to find the limit, we will plug $ a $ into the function and then simplify. a) Since, $ \lim_\limits{x\to 1^{-}} x=1$ when $ x \lt 1$ $\lim_\limits{x\to 1^{-}} x+6=1+6=7$ b) Since, $ \lim_\limits{x\to 1^{+}} x=1$ when $ x \gt 1$ $\lim_\limits{x\to 1^{+}} x+9=1+9=10$ c) From part (a) and (b) $\lim_\limits{x\to 1^{-}} \neq \lim_\limits{x\to 1^{+}}$ So, the limit does not exist.
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