Chapter 1: Q. 10 (page 97)

Use interval notation to fill in the blanks that follow. Your
answers will involve $δ, ε, N, and / or M$ .
If $\lim_{x \to \infty} f (x) = - \infty$ then for allrole="math" localid="1649070353117" $M > 0$ there is somerole="math" localid="1649070361631" $N > 0$ such that if $x \in_then \in_$ .

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

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

Step 2. Explanation.

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

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

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

$x \in (N, \infty) then f (x) \in (- \infty, M)$ .

Step 3. Statement.

Therefore, statement will be written as:

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

$x \in (N, \infty) then f (x) \in (- \infty, M)$ .

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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 $\lim_{x \to \infty} f (x) = - \infty$ then for allrole="math" localid="1649070353117" $M > 0$ there is somerole="math" localid="1649070361631" $N > 0$ 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.Iflimx→∞f(x)=-∞then for allrole="math" localid="1649070353117" M>0there is somerole="math" localid="1649070361631" N>0 such that ifx∈_____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

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Probability and Statistics

Theoretical and Mathematical Physics

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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 $\lim_{x \to \infty} f (x) = - \infty$ then for allrole="math" localid="1649070353117" $M > 0$ there is somerole="math" localid="1649070361631" $N > 0$ such that if $x \in_then \in_$ .