   Chapter 2, Problem 20RQ ### 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.If f(x) > 1 for all and lim x → 0 f ( x ) exists, then lim x → 0 f ( x ) > 1.

To determine

Whether the statement, “If f(x)>1 for all x and limx0f(x) exists, then limx0f(x)>1” is true or false.

Explanation

Reason:

The given statement is false since the below example disproves the given statement.

Let f(x)={x4+1ifx0 3if x=0

Here, for any x in , f(x)>1 and if x0, f(x)=x4+1 is a polynomial and it is continuous everywhere on its domain

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