Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Preliminary Questions - Page 72: 3


If $f$ is continuous at $x=c,$ then, by definition, $\lim _{x \rightarrow c} f(x)=f(c)$.

Work Step by Step

In other words, the limit of a continuous function at $x=c$ is the value of the function at $x=c .$ The "simplify and plug-in" strategy is based on simplifying a function which is indeterminate to a continuous function. Once the simplification has been made, the limit of the remaining continuous function is obtained by evaluation.
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