Chapter 1: Q. 9 (page 97)

Use interval notation to fill in the blanks that follow. Your
answers will involve $δ, ε, N, and / or M$ .
If $\lim_{x \to \infty} f (x) = 2$ then for all localid="1649070162044" $ε > 0$ there is somelocalid="1649070122210" $N > 0$ such that if $x \in_then \in_$ .

Short Answer

Expert verified

If $\lim_{x \to \infty} f (x) = 2$ then for all $ε > 0$ , there is some $N > 0$ such that if, $x \in (N, \infty) then f (x) \in (2 - ε, 2 + ε)$ .

Step by step solution

Step 1. Given information.

The given function is $\lim_{x \to \infty} f (x) = 2$ .

Step 2. Explanation.

From the given expression, we have, $c = \infty, L = 2$ .

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

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

$x \in (N, \infty) then f (x) \in (2 - ε, 2 + ε)$ .

Step 3. Statement.

Therefore, statement will be written as:

If $\lim_{x \to \infty} f (x) = 2$ then for all $ε > 0$ , there is some localid="1649070193596" $N > 0$ such that if, $x \in (N, \infty) then f (x) \in (2 - ε, 2 + ε)$ .

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Use interval notation to fill in the blanks that follow. Your
answers will involve $δ, ε, N, and / or M$ .
If $\lim_{x \to \infty} f (x) = 2$ then for all localid="1649070162044" $ε > 0$ there is somelocalid="1649070122210" $N > 0$ such that if $x \in_then \in_$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

Step 3. Statement.

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Use interval notation to fill in the blanks that follow. Youranswers will involveδ,ε,N,and/orM.If limx→∞f(x)=2then for all localid="1649070162044" ε>0there is somelocalid="1649070122210" N>0such that if x∈_____then∈_____.

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

Discrete Mathematics

Calculus

Mechanics Maths

Pure Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Use interval notation to fill in the blanks that follow. Your
answers will involve $δ, ε, N, and / or M$ .
If $\lim_{x \to \infty} f (x) = 2$ then for all localid="1649070162044" $ε > 0$ there is somelocalid="1649070122210" $N > 0$ such that if $x \in_then \in_$ .