Question 1

Which of the following statements best describes the meaning of $$\lim\limits_{x 	o \infty} f(x) = L$$?

Accepted Answer

As $$x$$ approaches infinity, $$f(x)$$ approaches the value $$L.$$

Question 2

Given the function $$f(x) = \frac{3x^2$ + 2x + 3}{2x^2$ + 3x + 5}$$, what is $$\lim\limits_{x 	o \infty} f(x)$$?

Accepted Answer

$$\frac{3}{2}$$

Question 3

Which theorem allows you to compute $$\lim\limits_{x 	o \infty} \frac{1}{x^n} = 0$$ for any $$n \u003e 0$$?

Accepted Answer

Power Rule for Limits at Infinity

Question 4

Evaluate $$\lim\limits_{x 	o \infty} \frac{1 - 5x^7$}{(x - 7)^7$}.$$

Accepted Answer

$$-5$$

Question 5

For the function $$f(x)$$ shown in the graph, which of the following is true about $$\lim\limits_{x 	o -\infty} f(x)$$?

Accepted Answer

The limit is the $$y-$$value where the graph flattens out as $$x$$ decreases without bound.

Question 6

Find $$\lim\limits_{x 	o \infty} \frac{\sqrt{x^2$ + x} - x}{x}.$$

Accepted Answer

$$\frac{1}{2}$$

Question 7

Which step is NOT part of the process for finding $$\lim\limits_{x 	o \infty} \frac{f(x)}{g(x)}$$ for rational functions?

Accepted Answer

Multiply numerator and denominator by $$x.$$

Question 8

Evaluate $$\lim\limits_{x 	o \infty} \sin(2x).$$

Accepted Answer

The limit does not exist.

Question 9

Find $$\lim\limits_{x 	o 7^-} \frac{1}{x - 7}.$$

Accepted Answer

$$-\infty$$

Question 10

Find $$\lim\limits_{x 	o 7^+} \frac{1}{x - 7}.$$

Accepted Answer

$$\infty$$

Question 11

Evaluate $$\lim\limits_{x 	o \infty} \frac{1}{5x}.$$

Accepted Answer

$$0$$

Question 12

Find $$\lim\limits_{x 	o \infty} \frac{5}{\sqrt{x^3$}}.$$

Accepted Answer

$$0$$

Question 13

Find $$\lim\limits_{x 	o 2^-} \frac{1}{x^2$ - 4}.$$

Accepted Answer

$$-\infty$$

Question 14

Find $$\lim\limits_{x 	o 2^+} \frac{1}{x^2$ - 4}.$$

Accepted Answer

$$\infty$$

Question 15

Suppose a medication's concentration in the bloodstream is modeled by $$C(t) = \frac{10}{t^2$ + 1}$$, where $$t is $$time in hours. What happens to the concentration as $$t 	o \infty$$?

Accepted Answer

It approaches $$0.$$

Question 16

A population model is given by $$P(t) = \frac{1000t}{t^2$ + 1}. $$What is $$\lim\limits_{t 	o \infty} P(t)$$?

Accepted Answer

$$0$$

Question 17

Which of the following is true about $$\lim\limits_{x 	o \infty} \frac{2x^3$ + 7x^2$ - 1}{8x^3$ - 3}$$?

Accepted Answer

$$\frac{2}{8}$$

Question 18

If $$\lim\limits_{x 	o \infty} f(x) = L$$ and $$\lim\limits_{x 	o \infty} g(x) = M$$, what is $$\lim\limits_{x 	o \infty} [f(x) + g(x)]$$?

Accepted Answer

$$L + M$$

Question 19

A chemical reaction rate is modeled by $$R(c) = \frac{c^2$}{c^2$ + 1}$$, where $$c is $$concentration. What is $$\lim\limits_{c 	o \infty} R(c)$$?

Accepted Answer

$$1$$

Limits at Infinity and Infinite Limits – Calculus Study Notes (Section 2.6)

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