Chapter 1: Q. 11 (page 97)

Use interval notation to fill in the blanks that follow. Your
answers will involve $δ, ε, N, and / or M$ .
If $\lim_{x \to 1^{+}} f (x) = \infty$ then for all $M > 0$ there is some role="math" localid="1649070911551" $δ > 0$ such that if $x \in_then \in_$ .

Short Answer

Expert verified

If $\lim_{x \to 1^{+}} f (x) = \infty$ then for all $M > 0$ there is some role="math" localid="1649070922171" $δ > 0$ such that if, $x \in (1, 1 + \infty) then f (x) \in (M, \infty)$ .

Step by step solution

Step 1. Given information.

The given function is $\lim_{x \to 1^{+}} f (x) = \infty$ .

Step 2. Explanation.

From the given expression, we have, $c = 1, L = \infty$ .

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

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

role="math" localid="1649071005696" $x \in (1, 1 + \infty) then f (x) \in (M, \infty)$ .

Step 3. Statement.

Therefore, statement will be written as:

If $\lim_{x \to 1^{+}} f (x) = \infty$ then for all $M > 0$ there is some $δ > 0$ such that if,

$x \in (1, 1 + \infty) then f (x) \in (M, \infty)$ .

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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 $\lim_{x \to 1^{+}} f (x) = \infty$ then for all $M > 0$ there is some role="math" localid="1649070911551" $δ > 0$ 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→1+f(x)=∞then for all M>0there is some role="math" localid="1649070911551" δ>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

Logic and Functions

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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 $\lim_{x \to 1^{+}} f (x) = \infty$ then for all $M > 0$ there is some role="math" localid="1649070911551" $δ > 0$ such that if $x \in_then \in_$ .