Use interval notation to fill in the blanks that follow. Youranswers will involveδ,ε , N, and/or M.If limx→∞f(x)=-∞ then for all role="math" localid="1649070353117" M>0 there is some role="math" localid="1649070361631" N>0 such that if x∈_____ then ∈_____.

If limx→∞f(x)=-∞ then for all M>0there is some N>0 such that if x∈N,∞ then f(x)∈-∞,M .

Q. 10 - Calculus | StudyQuestionHub

Use interval notation to fill in the blanks that follow. Your

answers will involve $δ, ε, N, and / or M$ .

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

Verified

Answer

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

1Step 1. Given information.

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

2Step 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,

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

3Step 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,

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