$$\lim_{x \to 0^+} f(x) = +\infty$$

Question 1

Consider the function $$f(x) = \frac{1}{x}. $$What is the value of $$\lim_{x 	o 0^-} f(x)$$?

Accepted Answer

$$-\infty$$

Question 2

Which of the following best describes an infinite limit?

Accepted Answer

A limit where the function increases or decreases without bound as $$x$$ approaches $$a$$

Question 3

Evaluate $$\lim_{x 	o 2} \frac{1}{(x-2)^2$}.$$

Accepted Answer

$$+\infty$$

Question 4

What is the value of $$\lim_{x 	o 0^+} \frac{1}{x}$$?

Accepted Answer

$$+\infty$$

Question 5

For which value of $$a$$ does $$\lim_{x 	o a} \frac{1}{(x-a)^n}$$ approach $$+\infty$$ for all even $$n$$?

Accepted Answer

For all $$a \in \mathbb{R}$$

Question 6

Which of the following statements is true about $$\lim_{x 	o 4} \frac{1}{(x-4)^2$}$$?

Accepted Answer

The limit is $$+\infty$$

Question 7

If $$\lim_{x 	o a} f(x) = +\infty$$, what does this mean about the behavior of $$f(x)$$ near $$x = a$$?

Accepted Answer

The function $$f(x)$$ increases without bound as $$x$$ approaches $$a$$

Question 8

Evaluate $$\lim_{x 	o 0} \frac{\sin(x)}{x}.$$

Accepted Answer

$$1$$

Question 9

Which of the following is a correct statement about lateral limits?

Accepted Answer

Lateral limits consider the behavior of a function as $$x$$ approaches $$a$$ from only one side

Question 10

Given $$f(x) = \frac{1}{x}$$, which of the following is true?

Accepted Answer

$$\lim_{x 	o 0^+} f(x) = +\infty$$

Question 11

Which graph best represents $$\lim_{x 	o a} \frac{1}{(x-a)^2$}$$?

Accepted Answer

A graph with a vertical asymptote at $$x = a$$ and the function approaching $$+\infty$$ from both sides

Question 12

If $$\lim_{x 	o a} f(x) = -\infty$$, what does this indicate?

Accepted Answer

The function $$f(x)$$ decreases without bound as $$x$$ approaches $$a$$

Question 13

Which of the following is an example of an infinite limit?

Accepted Answer

$$\lim_{x 	o 0} \frac{1}{x}$$

Question 14

What is the value of $$\lim_{x 	o 0} \frac{1}{x^2$}$$?

Accepted Answer

$$+\infty$$

Question 15

Which of the following is true about $$\lim_{x 	o a} \frac{1}{(x-a)^n}$$ for odd $$n$$?

Accepted Answer

The limit approaches $$+\infty$$ from one side and $$-\infty$$ from the other

Infinite Limits and Their Properties

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