Chapter 2.7, Problem 17E

Finding a symmetric interval Let $f(x)=\frac{2x^2-2}{x-1}$ and note that $\underset{x\to 1}{\lim }f(x)=4$. For each value of ε, use a graphing utility to find all values of δ > 0 such that |f(x) – 4| < ε whenever 0 < |x – 1| < δ.

1. a. ε = 2
2. b. ε = 1
3. c. For any ε > 0, make a conjecture about the value of δ that satisfies the preceding inequality.