Chapter 2: Limits and Continuity - Section 2.3 - The Precise Definition of a Limit - Exercises 2.3 - Page 65: 2

$\delta=1$

See graph; we can find $|c-a|=|2-1|=1$ and $|c-b|=|2-7|=5$. We choose $\delta=1$ (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.