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: 5

Answer

$\delta=\frac{1}{18}$
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Work Step by Step

See graph; we can find $|c-a|=|1/2-4/9|=\frac{1}{18}$ and $|c-b|=|1/2-4/7|=\frac{1}{14}$. We choose $\delta=\frac{1}{18}$ (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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