Chapter 2.7, Problem 14E

Finding δ for a given ε using a graph Let g(x) = 2x³ − 12x² + 26x + 4 and note that $\underset{x\to 2}{\lim }g(x)=24$. For each value of ε, use a graphing utility to find all values of δ > 0 such that |g(x) – 24| < ε whenever 0 < |x − 2| < δ. Sketch graphs illustrating your work.

1. a. ε = 1
2. b. ε = 0.5