Q. 8 Use interval notation to fill in... [FREE SOLUTION]

Chapter 1: Q. 8 (page 97)

Use interval notation to fill in the blanks that follow. Your
answers will involve $未, 蔚, N, and / or M$ .
If $\lim_{x 鈫� 3^{-}} f (x) = 1$ then for all $蔚 > 0$ there is some $未 > 0$ such that if $x 鈭�_then 鈭�_$ .

Short Answer

Expert verified

If $\lim_{x 鈫� 3^{-}} f (x) = 1$ then for all epsilon positive, there exists a delta positive such that if, $x 鈭� (3 - 未, 3) 鈭� (3, 3 + 未) Then f (x) 鈭� (1 - 蔚, 1 + 蔚)$ .

Step by step solution

Step 1. Given information.

The given function is $\lim_{x 鈫� 3^{-}} f (x) = 1$ .

Step 2. Explanation.

From the given expression, we have, $c = 3, L = 1$

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

For all epsilon positive, there exists a delta positive such that if,

$x 鈭� (3 - 未, 3) 鈭� (3, 3 + 未) Then f (x) 鈭� (1 - 蔚, 1 + 蔚)$ .

Step 3. Statement.

Therefore, statement will be written as:

If $\lim_{x 鈫� 3^{-}} f (x) = 1$ then for all epsilon positive, there exists a delta positive such that if, $x 鈭� (3 - 未, 3) 鈭� (3, 3 + 未) Then f (x) 鈭� (1 - 蔚, 1 + 蔚)$ .

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91影视

Use interval notation to fill in the blanks that follow. Your
answers will involve $未, 蔚, N, and / or M$ .
If $\lim_{x 鈫� 3^{-}} f (x) = 1$ then for all $蔚 > 0$ there is some $未 > 0$ such that if $x 鈭�_then 鈭�_$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

Step 3. Statement.

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Most popular questions from this chapter

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91影视

Use interval notation to fill in the blanks that follow. Youranswers will involve未,蔚,N,and/orM.Iflimx鈫�3-f(x)=1then for all蔚>0there is some未>0 such that ifx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

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Logic and Functions

Mechanics Maths

Applied Mathematics

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 $\lim_{x 鈫� 3^{-}} f (x) = 1$ then for all $蔚 > 0$ there is some $未 > 0$ such that if $x 鈭�_then 鈭�_$ .