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

Study Guide - Practice Questions