Let and note that For each value of , use a graphing utility to find all values of > 0 such that |f(x) -

Let

and note thatFor each value of ε, use a graphing utility to find all values of  δ > 0 such that |f(x) - 2| < ε whenever 0 < |x - 3| < δ.

a. ε = 1/2

b. ε = 1/4

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

zx + 1 x + ifx > 3 if x < 3 f(x) = lim f(x) = 2. x3