   Chapter 1.7, Problem 2E

Chapter
Section
Textbook Problem

Use the given graph of f to find a number δ such that i f   0 < | x − 3 | < δ   t h e n   | f ( x ) − 2 | < 0.5 To determine

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

Explanation

Given:

If 0<|x3|<δ, then |f(x)2|<0.5.

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)2|<0.5.

By absolute value definition, 0.5<f(x)2<0.5.

Simplify the inequality by adding 2 on each side,

20.5<2+f(x)2<2+0

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