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 2.3 - The Precise Definition of a Limit - Exercises 2.3 - Page 65: 1

Answer

$\delta=2$

Work Step by Step

See graph; we can find $|c-a|=|5-1|=4$ and $|c-b|=|5-7|=2$. We choose $\delta=2$ (smaller of the two values) so that for all $x$, when $0\lt|x-c|\lt\delta$, we have $a\lt x\lt b$ as can be seen from the figure.
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