   Chapter 2.5, Problem 67E ### 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

# For what values of x is f continuous? f ( x ) = { 0   if   x   is rational 1   if   x   is irrational

To determine

To find: The values of x for which the function f(x)={0if x1if x

is continuous

Explanation

For a rational number α, choose any real number δ>0

f(α)=0

Consider the interval (αδ,α+δ)

The above interval has infinity many irrational points. Thus, there are infinity many irrational points x satisfying 0<|xα|<δ and |f(x)f(α)|=1 with f(x)=1

So,limxαf(x)f(α)

Thus, limxαf(x) does not exist

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 49-62, find the indicated limit, if it exists. 58. limz2z38z2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Solve the equations in problem 1-6. 2.

Mathematical Applications for the Management, Life, and Social Sciences

#### 01e2xdx= a) 2e2 1 b) `e2 1 c) 12e2 d) 12(e21)

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