# Chapter 2: Limits and Continuity - Section 2.3 - The Precise Definition of a Limit - Exercises 2.3 - Page 65: 8

$\delta=0.1$

#### Work Step by Step

We see from the graph that in order for $f(x)$ to be within $\epsilon=0.15$ of $L=7.5$, we must have $$-3.1 \lt x \lt -2.9.$$ Subtracting $-3$ from all three sides gives $$-0.1 \lt x-(-3) \lt 0.1.$$ Hence for $\delta = 0.1$, $$0 \lt |x-(-3)| \lt \delta \implies 0 \lt |f(x)-7.5| \lt \epsilon.$$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.