   Chapter 2.4, Problem 1E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Use the given graph of f to find a number δ such thatif |x – 1| < δ then |f(x) – 1| < 0.2 To determine

To find: The value of a number δ by using the graph of f.

Explanation

Given:

If |x1|<δ, then |f(x)1|<0.2.

Definition used:

If for every number ε>0 there is a number δ>0 such that if 0<|xa|<δ, then |f(x)L|<ε.

Absolute value inequality: If |x|<a,a>0, then a<x<a.

Calculation:

Consider |f(x)1|<0.2.

By absolute value definition, 0.2<f(x)1<0.2.

Simplify the inequality by adding 1 on each side,

10.2<1+f(x)1<1+0

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