Q: Jimmy’s Music Shop has cost function $C(x) = 77x + 1900$ and revenue function $R(x) = 146x$. What is the profit from selling $x = 80$ keyboards?

$P(80) = 146 \times 80 - (77 \times 80 + 1900)$

Q: If $f$ is continuous at $x = -10$, which of the following must be true?

$\lim_{x \to -10} f(x) = f(-10)$

Question 1

Which of the following equations represents a function?

Accepted Answer

$y = x^2 - 8x + 7$

Question 2

Given $f(x) = x^2 - 8x + 7$, what is the vertex of the parabola?

Accepted Answer

$(4, -9)$

Question 3

Find the domain of the function $f(x) = \frac{x-2}{6x-12}$.

Question 4

If $\lim_{x 	o a} f(x)$ exists, which of the following must be true?

Accepted Answer

$f(x)$ approaches a finite value as $x$ approaches $a$

Question 5

An investor puts $9900 into an account that pays 9% interest compounded continuously. How much will be in the account after 4 years?

Accepted Answer

$9900 	imes e^{0.36}$

Question 6

Let $f(x) = 2x^2 - 9x + 79$. What is $f'(x)$?

Accepted Answer

$4x - 9$

Question 7

Given $f(x) = 3x^2 - 9x - 66$, find the equation of the tangent line to $f(x)$ at the point $(6, -12)$.

Question 8

Jimmy’s Music Shop has cost function $C(x) = 77x + 1900$ and revenue function $R(x) = 146x$. What is the profit from selling $x = 80$ keyboards?

Accepted Answer

$P(80) = 146 	imes 80 - (77 	imes 80 + 1900)$

Question 9

Given $P(t) = 0.6t^2 + 0.4t + 75$, where $t$ is the number of years since 2010, what is the average rate of change of the poster price between 2015 and 2024?

Accepted Answer

$\frac{P(14) - P(5)}{14 - 5}$

Question 10

If $\lim_{x 	o -4} H(x)$ exists and $H(-4)$ exists, which of the following is necessary for $H$ to be continuous at $x = -4$?

Accepted Answer

$\lim_{x 	o -4} H(x) = H(-4)$

Question 11

For the function $f(x) = x^2 - 8x + 7$, what is the line of symmetry?

Accepted Answer

$x = 4$

Question 12

Given $\lim_{x 	o \infty} \frac{5x^2 - 9x + 8}{4x^2 - 8x + 1}$, what is the value of the limit?

Accepted Answer

$\frac{5}{4}$

Question 13

If $f$ is continuous at $x = -10$, which of the following must be true?

Accepted Answer

$\lim_{x 	o -10} f(x) = f(-10)$

Question 14

For the function $f(x) = x^2 - 8x + 7$, what are the $x$-intercepts?

Accepted Answer

$x = 1$ and $x = 7$

Question 15

If $f(x)$ is continuous at $x = 2$, which of the following is true?

Accepted Answer

$\lim_{x 	o 2} f(x) = f(2)$

Question 16

Given $C(x) = 77x + 1900$ and $R(x) = 146x$, what is the average unit profit function $F(x)$?

Accepted Answer

$F(x) = \frac{R(x) - C(x)}{x}$

Question 17

If $\lim_{x 	o a} f(x) = f(a)$, which of the following is true?

Accepted Answer

$f(x)$ is continuous at $x = a$

Question 18

Let $f(x) = 2x^2 - 9x + 79$. What is the value of $f'(2)$?

Business Calculus: Functions, Limits, Continuity, and Applications

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