Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.2 - Limit of a Function and Limit Laws - Exercises 2.2 - Page 56: 10


The limit values can not be determined $\lim\limits_{x \to 1}f(x)$ until we have the values of function $f(x)$ near x = 1.

Work Step by Step

The existence and non-existence of the limit $\lim\limits_{x \to 1}f(x)$ does not depend on whether the function is defined or not defined at the point near $x=c$. Thus, when $f(1) = 5$, then it is not necessary that the limit would exist as $x \to 1$.
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