Chapter 2: Limits and Continuity - Section 2.3 - The Precise Definition of a Limit - Exercises 2.3 - Page 65: 3

$\delta=\frac{1}{2}$

See graph; we can find $|c-a|=|-3+7/2|=1/2$ and $|c-b|=|-3+1/2=|=5/2$. We choose $\delta=\frac{1}{2}$ (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.