Problem 24E

Each of Exercises 15–30 gives a function ƒ(x) and numbers L, c, and In each case, find an open interval about c on which the inequality holds. Then give a value for δ > 0 such that for all x satisfying 0 < |x – c| < δ the inequality holds.

ƒ(x) = 1/x, L = -1, c = -1, = 0.1

Solution

Step 1 of 3

Given that

We have to find an open interval about on which the inequality |ƒ(x) – L| < ϵ holds. Then give a value for δ > 0 such that for all x satisfying 0 < | x – c | < δ the inequality |ƒ(x) – L| < ϵ holds.