Use interval notation to fill in the blanks that follow. Youranswers will involveδ,ε , N, and/or M.If limx→1+f(x)=∞ then for all M>0 there is some role="math" localid="1649070911551" δ>0 such that if x∈_____ then ∈_____.

If limx→1+f(x)=∞then for all M>0 there is some role="math" localid="1649070922171" δ>0 such that if,x∈1,1+∞ then f(x)∈M,∞.

Q. 11 - Calculus | StudyQuestionHub

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 $δ > 0$ such that if $x \in_____then \in_____$ .

Verified

Answer

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

1Step 1. Given information.

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

2Step 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,

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

3Step 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,

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