Question 1

Which of the following best describes an infinite limit at $$x = a$$?

Accepted Answer

The function increases or decreases without bound as $$x$$ approaches $$a.$$

Question 2

Given $$f(x) = \frac{x^2$ - 9x + 14}{x^2$ - 5x + 6}$$, what is the vertical asymptote of $$f(x)$$?

Accepted Answer

$$x = 3$$

Question 3

For the function $$f(x) = \frac{x-5}{x^2$-25}$$, which value of $$x is a $$vertical asymptote?

Accepted Answer

$$x = -5$$

Question 4

Which of the following functions has a vertical asymptote at $$x = 0$$?

Accepted Answer

$$f(x) = \frac{x^2$-3x+2}{x^9$(x-1)}$$

Question 5

The function $$g(	heta) = 	an\left(\frac{\pi 	heta}{10}ight)$$ has vertical asymptotes at which values of $$	heta$$?

Accepted Answer

$$	heta = 5 + 10k$$

Question 6

Given the graph of $$f(x)$$ with a vertical asymptote at $$x = 1$$, what is $$\lim_{x 	o 1} f(x) if $$both sides approach $$+\infty$$?

Accepted Answer

$$\infty$$

Question 7

If $$\lim_{x 	o 3^-} f(x) = \infty$$ and $$\lim_{x 	o 3^+} f(x) = -\infty$$, what is $$\lim_{x 	o 3} f(x)$$?

Accepted Answer

Does not exist

Question 8

Evaluate $$\lim_{x 	o 4} \frac{x-5}{(x-4)^2$}.$$

Accepted Answer

$$-\infty$$

Question 9

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

Accepted Answer

$$-\infty$$

Question 10

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

Accepted Answer

$$\infty$$

Question 11

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

Accepted Answer

Does not exist

Question 12

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

Accepted Answer

$$\infty$$

Question 13

Evaluate $$\lim_{x 	o 0^+} \csc x.$$

Accepted Answer

$$\infty$$

Question 14

Which of the following statements about vertical asymptotes is TRUE?

Accepted Answer

Vertical asymptotes occur at $$x-$$values that make the denominator zero in fully simplified rational functions.

Question 15

A chemical reaction rate is modeled by $$R(t) = \frac{1}{t-2}$$, where $$t is $$time in seconds. What happens to the reaction rate as $$t$$ approaches $$2$$ from the right?

Accepted Answer

The reaction rate approaches $$\infty.$$

Question 16

A medical dosage function is given by $$D(x) = \frac{5}{x-1}$$, where $$x is $$the number of hours after administration. What is the behavior of $$D(x) as$$ $$x$$ approaches $$1$$ from the left?

Accepted Answer

$$D(x)$$ approaches $$-\infty.$$

Question 17

Which of the following is NOT a possible cause of a vertical asymptote in a function?

Accepted Answer

A removable discontinuity (hole) in the function.

Infinite Limits and Vertical Asymptotes

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