Question 1

A company models its profit with the function $$P(x) = \frac{x^2$ - 3}{2x^2$ - x}$$, where $$x is $$the number of units sold. What is $$\lim_{x 	o 2} P(x)$$?

Accepted Answer

$$\frac{1}{4}$$

Question 2

Given $$f(x) = 3 - 2x^2$, use the four-step process to find f$$'(1)$$.

Accepted Answer

$$-4$$

Question 3

Evaluate $$\lim_{x 	o \infty} \frac{7x^4$ - 4x^2$}{5x^4$ + 2}.$$

Accepted Answer

$$\frac{7}{5}$$

Question 4

A manufacturer uses the function $$M(x) = \frac{x-4}{x^2$-9} to $$model cost per item. For which values of $$x is$$ $$M(x)$$ continuous?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 5

Let $$f(x) = \frac{x-12}{x^2$-12x}. $$What is $$\lim_{x 	o 12} f(x)$$?

Accepted Answer

$$\frac{1}{144}$$

Question 6

Suppose $$G(x) is a $$function such that $$\lim_{x 	o 1} G(x) = 3. $$What does this mean?

Accepted Answer

As $$x$$ approaches $$1$$, $$G(x)$$ approaches $$3.$$

Question 7

A business models its revenue with $$R(x) = \frac{x^2$ - 3x + 2}{x^2$ + 2}. $$What is $$\lim_{x 	o \infty} R(x)$$?

Accepted Answer

$$1$$

Question 8

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

Accepted Answer

$$-1$$

Question 9

If $$f(x) is $$continuous everywhere except at $$x = 2$$, which of the following could be the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 10

A company’s cost function is $$C(x) = \frac{x^2$ - 12}{x^2$ - 12x}. $$What is $$\lim_{x 	o 12} C(x)$$?

Accepted Answer

$$\frac{1}{12}$$

Question 11

Given $$f(x) = 3 - 2x^2$, what is f$$'(2)$$?

Accepted Answer

$$-8$$

Question 12

Evaluate $$\lim_{x 	o 0} f(x)$$ for $$f(x) = 0.$$

Accepted Answer

$$0$$

Question 13

A function $$f(x) is $$defined as $$f(x) = \frac{x^2$ - 3}{2x^2$ - x}. $$What is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$0$$

Question 14

If $$f(x) = 3 - 2x^2$, what is f$$'(3)$$?

Accepted Answer

$$-12$$

Question 15

Which of the following statements is true about the function $$M(x) = \frac{x-4}{x^2$-9}$$?

Accepted Answer

It is discontinuous at $$x = 3$$ and $$x = -3.$$

Question 16

A business models its cost with $$C(x) = \frac{x^2$ - 12}{x^2$ - 12x}. $$What is $$\lim_{x 	o 0} C(x)$$?

Accepted Answer

$$-1$$

Question 17

If $$f(x) = 3 - 2x^2$, what is the derivative f$$'(x)$$?

Accepted Answer

$$-4x$$

Question 18

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

Accepted Answer

$$1$$

Question 19

If $$f(x) is $$continuous on $$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$, which of the following is true?

Accepted Answer

$$f(x) is $$undefined at $$x = 3$$ and $$x = -3.$$

Limits, Continuity, and Derivatives in Business Calculus: Study Guide

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