   Chapter 2, Problem 19RQ ### 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

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.Let f be a function such that lim x → 0 f ( x ) = 6. Then there exists a positive number δ such that if 0 < | x | < δ, then | f(x) – 6| < 1.

To determine

Whether the statement, “Let f be a function such that limx0f(x)=6. Then there exists a number δ such that if 0<|x|<δ, then |f(x)6|<1” is true or false.

Explanation

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”.

Reason:

Given that, f be a function such that limx0f(x)=6.

Here, a=0 and L=6

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 