Chapter 2.7, Problem 1QC

In Example 1, find a positive number δ satisfying the statement

$|f\left(x\right)-5|<\frac{1}{100}\text{ whenever }0\text{<|}x-3|<\delta .$

Example 1 Determining Values of δ from a Graph

Figure 2.59 shows the graph of a linear function f with $\underset{x\to 3}{\lim }f\left(x\right)=5$. For each value of ε > 0, determine a value of δ > 0 satisfying the statement

Figure 2.59

|f(x) − 5| < ε whenever 0 < |x − 3| < δ.