   Chapter 2.4, Problem 13E ### 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

# (a) Find a number δ such that if |x – 2| <δ, then |4x – 8| < ε, where ε = 0.1.(b) Repeat part (a) with ε = 0.01

(a)

To determine

To find: The number δ such that |4x8|<ε whenever |x2|<δ.

Explanation

Given:

Let ε be a positive integer and ε=0.1.

Definition used:

“Let f be a function defined on some open interval that contains the number a, except possibly at a itself. Then, the limit of f(x) as x approaches a is L, limxaf(x)=L if for every number ε>0 there is a number δ>0 such that if 0<|xa|<δ then |f(x)L|<ε”.

Calculation:

Let ε be a given positive integer. Here, f(x)=4x, a=2 and L=8.

By the definition of ε and δ, it is enough to find a number δ such that,

if 0<|x2|<δ, then |4x8|<ε=0

(b)

To determine

To find: The number δ such that |4x8|<ε whenever |x2|<δ.

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