Q: Suppose $$f(x) is $$defined near $$x = a$$ and as $$x$$ approaches $$a$$, $$f(x)$$ decreases without bound. Which of the following best describes this situation?

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

Q: Given the graph in the first image, what is the correct mathematical statement for the limit as $$x$$ approaches $$a$$?

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

Q: Which of the following statements is true about vertical asymptotes?

A vertical asymptote occurs at $$x = a if$$ $$\lim_{x \to a} f(x) = \pm\infty.$$

Q: If $$\lim_{x \to a^-} f(x) = \infty$$ and $$\lim_{x \to a^+} f(x) = -\infty$$, what can you conclude about $$\lim_{x \to a} f(x)$$?

$$\lim_{x \to a} f(x)$$ does not exist

Question 1

Suppose $$f(x) is $$defined near $$x = a$$ and as $$x$$ approaches $$a$$, $$f(x)$$ decreases without bound. Which of the following best describes this situation?

Accepted Answer

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

Question 2

Given the graph in the first image, what is the correct mathematical statement for the limit as $$x$$ approaches $$a$$?

Accepted Answer

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

Question 3

Which of the following statements is true about vertical asymptotes?

Accepted Answer

A vertical asymptote occurs at $$x = a if$$ $$\lim_{x 	o a} f(x) = \pm\infty.$$

Question 4

For the function $$g(x)$$ shown in the second image, what is $$\lim_{x 	o 2^-} g(x)$$?

Accepted Answer

$$\infty$$

Question 5

For the function $$g(x)$$ shown in the second image, what is $$\lim_{x 	o 2^+} g(x)$$?

Accepted Answer

$$-\infty$$

Question 6

For the function $$g(x)$$ shown in the second image, what is $$\lim_{x 	o 2} g(x)$$?

Accepted Answer

The limit does not exist

Question 7

For the function $$g(x)$$ shown in the second image, what is $$\lim_{x 	o 4^-} g(x)$$?

Accepted Answer

$$-\infty$$

Question 8

For the function $$g(x)$$ shown in the second image, what is $$\lim_{x 	o 4^+} g(x)$$?

Accepted Answer

$$-\infty$$

Question 9

For the function $$g(x)$$ shown in the second image, what is $$\lim_{x 	o 4} g(x)$$?

Accepted Answer

$$-\infty$$

Question 10

Suppose $$f(x) = \frac{x^2$ - 4x + 3}{x^2$ - 1}. $$Which of the following is a vertical asymptote of $$f(x)$$?

Accepted Answer

$$x = 1$$

Question 11

Evaluate $$\lim_{x 	o 1} \frac{x^2$ - 4x + 3}{x^2$ - 1}.$$

Accepted Answer

$$\infty$$

Question 12

Which of the following best describes the behavior of $$f(x) = \frac{1}{x - 2} as$$ $$x$$ approaches $$2$$ from the left?

Accepted Answer

$$f(x)$$ approaches $$-\infty$$

Question 13

If $$\lim_{x 	o a^-} f(x) = \infty$$ and $$\lim_{x 	o a^+} f(x) = -\infty$$, what can you conclude about $$\lim_{x 	o a} f(x)$$?

Accepted Answer

$$\lim_{x 	o a} f(x)$$ does not exist

Question 14

A chemical reaction rate is modeled by $$R(t) = \frac{1}{t - 5}$$, where $$t is $$time in seconds. What happens to the reaction rate as $$t$$ approaches $$5$$ from below?

Accepted Answer

The reaction rate approaches $$-\infty$$

Question 15

Which of the following is NOT a correct way to express an infinite limit?

Accepted Answer

$$\lim_{x 	o a} f(x) = 0$$

Calculus I: Infinite Limits and Vertical Asymptotes

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