Q. 9 Use interval notation to fill in... [FREE SOLUTION]

Chapter 1: Q. 9 (page 97)

Use interval notation to fill in the blanks that follow. Your
answers will involve $未, 蔚, N, and / or M$ .
If $\lim_{x 鈫� 鈭�} f (x) = 2$ then for all localid="1649070162044" $蔚 > 0$ there is somelocalid="1649070122210" $N > 0$ such that if $x 鈭�_then 鈭�_$ .

Short Answer

Expert verified

If $\lim_{x 鈫� 鈭�} f (x) = 2$ then for all $蔚 > 0$ , there is some $N > 0$ such that if, $x 鈭� (N, 鈭�) then f (x) 鈭� (2 - 蔚, 2 + 蔚)$ .

Step by step solution

Step 1. Given information.

The given function is $\lim_{x 鈫� 鈭�} f (x) = 2$ .

Step 2. Explanation.

From the given expression, we have, $c = 鈭�, L = 2$ .

The limit expression can be written as a formal statement as below,

For all epsilon positive, there is some $N > 0$ such that if,

$x 鈭� (N, 鈭�) then f (x) 鈭� (2 - 蔚, 2 + 蔚)$ .

Step 3. Statement.

Therefore, statement will be written as:

If $\lim_{x 鈫� 鈭�} f (x) = 2$ then for all $蔚 > 0$ , there is some localid="1649070193596" $N > 0$ such that if, $x 鈭� (N, 鈭�) then f (x) 鈭� (2 - 蔚, 2 + 蔚)$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Use interval notation to fill in the blanks that follow. Your
answers will involve $未, 蔚, N, and / or M$ .
If $\lim_{x 鈫� 鈭�} f (x) = 2$ then for all localid="1649070162044" $蔚 > 0$ there is somelocalid="1649070122210" $N > 0$ such that if $x 鈭�_then 鈭�_$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

Step 3. Statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Logic and Functions

Discrete Mathematics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Use interval notation to fill in the blanks that follow. Youranswers will involve未,蔚,N,and/orM.If limx鈫�鈭�f(x)=2then for all localid="1649070162044" 蔚>0there is somelocalid="1649070122210" N>0such that if x鈭�_____then鈭�_____.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

Step 3. Statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Logic and Functions

Discrete Mathematics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Use interval notation to fill in the blanks that follow. Your
answers will involve $未, 蔚, N, and / or M$ .
If $\lim_{x 鈫� 鈭�} f (x) = 2$ then for all localid="1649070162044" $蔚 > 0$ there is somelocalid="1649070122210" $N > 0$ such that if $x 鈭�_then 鈭�_$ .