Precalculus (6th Edition) Blitzer

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

Chapter 11 - Section 11.1 - Finding Limits Using Tables and Graphs - Exercise Set - Page 1142: 93


$$f(x)=\begin{cases}x+3, & x \lt 2 \\ x+3, & x \gt 2 \end{cases}$$ (Other answers are possible.)

Work Step by Step

Consider the function$$f(x)=\begin{cases}x+3, & x \lt 2 \\ x+3, & x \gt 2 \end{cases}.$$This function is not defined at $x=2$. Nonetheless, the limit at $x=2$ exists and equals: $$\lim_{x \to 2}f(x)=5.$$ Please note that in the definition of the limit, $\lim_{x \to a}f(x)$, the function $f$ does not need to be defined at $x=a$.
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