5 Jan 2022
Problem 37b
Page 119
Section 2.9: The Formal Definition of a Limit
Chapter 2: Limits and Derivatives
Textbook ExpertVerified Tutor
5 Jan 2022
Given information
We are given,
We have to show that 
is continuous at 
if is irrational.
Step-by-step explanation
Step 1.
Let be an irrational number. Given 
, let 
be a positive integer so that 
.
be an irrational number. Given , let be a positive integer so that .Consider the set 
of all rational numbers 
so that 
(there is a finite number of such numbers).
of all rational numbers so that (there is a finite number of such numbers).
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805