Question 1

Let $$p(x) = 7x^5$ - 3x^2$ + 4. $$What is $$\lim_{x 	o \infty} p(x)$$?

Accepted Answer

$$\infty$$

Question 2

Evaluate $$\lim_{x 	o -\infty} (-2x^3$ + 5x - 1).$$

Accepted Answer

$$\infty$$

Question 3

Given $$f(x) = \dfrac{4x^2$ + 7x + 1}{2x^2$ - 3x + 5}$$, what is the horizontal asymptote of $$f(x)$$?

Accepted Answer

$$y = 2$$

Question 4

Which of the following best describes the horizontal asymptote of $$f(x) = \dfrac{3x^2$ + 1}{x^3$ - 2}$$?

Accepted Answer

$$y = 0$$

Question 5

Find $$\lim_{x 	o \infty} \left(2 + \dfrac{10}{x^3$}ight).$$

Accepted Answer

$$2$$

Question 6

Suppose $$f(x) = \dfrac{x^3$ - 2x}{2x + 4}. $$What is $$\lim_{x 	o \infty} f(x)$$?

Accepted Answer

$$\infty$$

Question 7

A chemical reaction rate is modeled by $$R(x) = \dfrac{50x^4$ + 4x^2$ - 1}{10x^4$ + 8x^2$ + 1}. As $$the concentration $$x$$ becomes very large, what does the reaction rate approach?

Accepted Answer

$$5$$

Question 8

For $$f(x) = \dfrac{x^2$ - 81}{x(x - 9)}$$, what is the vertical asymptote?

Accepted Answer

$$x = 0$$

Question 9

Given $$f(x) = \dfrac{x^2$ - 81}{x^2$ - 9x}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 1$$

Question 10

A population model is given by $$P(x) = 3x^3$ - 6x^2$ + x - 10. $$What is $$\lim_{x 	o -\infty} P(x)$$?

Accepted Answer

$$-\infty$$

Question 11

Which statement is true about the horizontal asymptote of $$f(x) = \dfrac{x^2$ - 2x}{2x + 4}$$?

Accepted Answer

There is no horizontal asymptote.

Question 12

Evaluate $$\lim_{x 	o \infty} \dfrac{3x^3$ + 2}{x^5$ - 1}.$$

Accepted Answer

$$0$$

Question 13

A medication's effectiveness is modeled by $$E(x) = 2 + \dfrac{10}{x^3$}. As $$the dosage $$x$$ increases without bound, what does the effectiveness approach?

Accepted Answer

$$2$$

Question 14

For $$f(x) = \dfrac{3x^3$ - 6x^2$ + x - 10}{x^3$}$$, what is $$\lim_{x 	o \infty} f(x)$$?

Accepted Answer

$$3$$

Question 15

Which of the following is true for the horizontal asymptote of $$f(x) = \dfrac{3x^2$ + 1}{x^3$ - 2}$$?

Accepted Answer

$$y = 0$$

Question 16

If the degree of the numerator is less than the degree of the denominator in a rational function, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 17

For $$f(x) = \dfrac{50x^4$ + 4x^2$ - 1}{10x^4$ + 8x^2$ + 1}$$, what is $$\lim_{x 	o \infty} f(x)$$?

Accepted Answer

$$5$$

Question 18

A rational function $$f(x) = \dfrac{p(x)}{q(x)}$$ has $$\deg(p(x)) \u003e \deg(q(x)). $$What can be said about its horizontal asymptote?

Accepted Answer

There is no horizontal asymptote.

Question 19

Evaluate $$\lim_{x 	o -\infty} (5x^4$ - 3x^3$ + 2).$$

Accepted Answer

$$\infty$$

Question 20

A rational function $$f(x) = \dfrac{ax^n + \ldots}{bx^n + \ldots}$$, where $$a$$ and $$b$$ are nonzero and $$n is $$the highest degree, has what horizontal asymptote?

Accepted Answer

$$y = \dfrac{a}{b}$$

Limits at Infinity and Horizontal Asymptotes 2.5

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