$$\{x \in \mathbb{R} : x \neq 2, x \neq -2 \}$$

$$\{x \in \mathbb{R} : x \neq 3 \}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

$$\{x \in \mathbb{R} : x 
eq 2, x 
eq -2 \}$$

Question 2

Given the function $$f(x) = e$$^{-x^2}$$, on which interval is the function concave up?

Accepted Answer

$$x \in \mathbb{R}$$

Question 3

If $$f(x) = \ln(x^2$ + 9)$$, what is the domain of $$f$$?

Accepted Answer

$$\{x \in \mathbb{R} \}$$

Question 4

Which of the following is the correct derivative of $$f(x) = \sin(3x)$$?

Accepted Answer

$$3\cos(3x)$$

Question 5

A population grows according to $$P(t) = P_0$ e$$^{kt}$$. If the population doubles in 5 years, what is the value of k$?

Accepted Answer

$$k = \ln(2)/5$$

Question 6

If $$f(x) = x^3$ + x^2$, on which interval is f$ concave down?

Accepted Answer

$$x \u003c -\frac{1}{3}$$

Question 7

Given the cost function $$C(q) = q^3$ - 9q^2$ + 27q + 8$$ and revenue function $$R(q) = 15q$$, what are the fixed costs?

Accepted Answer

$$8$$

Question 8

Which of the following is the correct formula for the tangent line to $$f(x) at$$ $$x = a$$?

Accepted Answer

$$y - f(a) = f'(a)(x - a)$$

Question 9

If $$f(x) = \ln(x - 1)$$, what is the domain of $$f$$?

Accepted Answer

$$\{x \in \mathbb{R} : x \u003e 1 \}$$

Question 10

Which of the following is the correct indefinite integral of $$\int x^6$ dx$$?

Accepted Answer

$$\frac{1}{7}x^7$ + C$$

Question 11

If $$f(x) = |x + 3|$$, what is the solution to $$|x + 3| = 2$$?

Accepted Answer

$$x = -1 or$$ $$x = -5$$

Question 12

Which of the following is the correct formula for the average value of a function $$f(x) on$$ $$[a, b]$$?

Accepted Answer

$$\frac{1}{b - a} \int_a^b f(x) dx$$

Question 13

If $$f(x) = x^2$ - 2x - 8$$, solve the inequality $$f(x) \leq 0$$ using the graph.

Accepted Answer

$$-2 \leq x \leq 4$$

Question 14

Which of the following is the correct derivative of $$f(x) = \ln(x^2$ + 4)$$?

Accepted Answer

$$\frac{2x}{x^2$ + 4}$$

Question 15

If $$f(x) = x^3$ + x^2$, on which interval is f$ increasing?

Accepted Answer

$$x \u003e -\frac{2}{3}$$

Question 16

Which of the following is the correct formula for compound interest compounded continuously?

Accepted Answer

$$A = P e$$^{rt}$$

Question 17

Given the function $$f(x) = \frac{2}{x - 3}$$, on which interval is $$f$$ continuous?

Accepted Answer

$$\{x \in \mathbb{R} : x 
eq 3 \}$$

Question 18

If $$f(x) = \ln(x)$$, what is the range of $$f$$?

Accepted Answer

$$\{y \in \mathbb{R} \}$$

Question 19

Which of the following is the correct product of a $$2 	imes 3$$ matrix and a $$3 	imes 2$$ matrix?

Accepted Answer

$$2 	imes 2$$ matrix

Calculus Study Guide: Functions, Derivatives, Extrema, and Integration

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