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

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

Given $$f(x) = \frac{1}{(x-a)^n}$$, for $$n$$ even and $$a \in \mathbb{R}$$, what is $$\lim_{x 	o a} f(x)$$?

Accepted Answer

$$+\infty$$

Question 6

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

Accepted Answer

The limit is $$+\infty$$

Question 7

Evaluate $$\lim_{x 	o 4} \frac{1}{(x-4)^2$}.$$

Accepted Answer

$$+\infty$$

Question 8

What is the value of $$\lim_{x 	o 0} \frac{\sin(x)}{x}$$?

Accepted Answer

$$1$$

Question 9

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 increases without bound

Question 10

Which of the following is an example of a function with an infinite limit at $$x = 0$$?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 11

For the function $$f(x) = \frac{1}{x}$$, which of the following statements is correct?

Accepted Answer

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

Question 12

Which of the following best describes the behavior of $$\frac{1}{(x-a)^2$} as$$ $$x$$ approaches $$a$$?

Accepted Answer

The function approaches $$+\infty$$

Question 13

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

Accepted Answer

The function decreases without bound as $$x$$ approaches $$a$$

Question 14

Evaluate $$\lim_{x 	o 0} \frac{1}{x^2$}.$$

Accepted Answer

$$+\infty$$

Question 15

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

Accepted Answer

The limit depends on the direction from which $$x$$ approaches $$a$$

Study Notes: Infinite Limits in Calculus

Study Guide - Practice Questions