Chapter 2.7, Problem 16E

Finding a symmetric interval The function f in the figure satisfies $\underset{x\to 4}{\lim }f(x)=5$. For each value of ε, find all values of δ > 0 such that

$|f(x)-5|<\epsilon \text{whenever}0<|x-4|<\delta .$ (3)

1. a. ε = 2
2. b. ε = 1
3. c. For any ε > 0, make a conjecture about the corresponding values of δ satisfying (3).