Chapter 2.7, Problem 13E

Finding δ for a given ε using a graph Let f(x) = x³ + 3 and note that $\underset{x\to 0}{\lim }f(x)=3$. For each value of ε, use a graphing utility to find all values of δ > 0 such that |f(x) – 3| < ε whenever 0 < |x – 0| < δ. Sketch graphs illustrating your work.

1. a. ε = 1
2. b. ε = 0.5