Q: If $$\lim_{x \to 2} f(x)$$ exists, which of the following must be true?

$$f(x)$$ approaches a finite value as $$x \to 2.$$

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 statements is TRUE about the function $$f(x) = \frac{2x-1}{6x-12}$$?

Accepted Answer

The domain is all real numbers except $$x = 2.$$

Question 2

Let $$f(x) = x^2$ - 8x + 7. $$What is the vertex of the parabola?

Accepted Answer

The vertex is at $$\left(4, -9\right).$$

Question 3

Suppose $$\lim_{x 	o -4} H(x)$$ exists and $$H(-4) is $$defined, but $$\lim_{x 	o -4} H(x) 
eq H(-4). $$What can you conclude about the continuity of $$H at$$ $$x = -4$$?

Accepted Answer

$$H is $$not continuous at $$x = -4.$$

Question 4

Evaluate $$\lim_{x 	o \infty} \frac{5x^2$ - 9x + 8}{4x^2$ - 8x + 1}.$$

Accepted Answer

$$\frac{5}{4}$$

Question 5

An investor puts $$\9900$ into an account that pays 9$$\%$$ interest compounded continuously. How much will be in the account after 4 years? (Use A$$ = $$Pe^{rt}$)

Accepted Answer

$$\14060.12$

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 $$(6, -12).$$

Accepted Answer

$$y = 27x - 174$$

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

$$5520$$

Question 9

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

Accepted Answer

$$10.8$$

Question 10

Which of the following is TRUE about the function $$f(x) = x^2$ - 8x + 7$$?

Accepted Answer

The parabola opens upward.

Question 11

If $$\lim_{x 	o 2} f(x)$$ exists, which of the following must be true?

Accepted Answer

$$f(x)$$ approaches a finite value as $$x 	o 2.$$

Question 12

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 13

Which of the following equations can be represented as a function of $$x$$?

Accepted Answer

$$y = x^2$ + 1$$

Question 14

If $$f(-10) = -3$$ and $$f(2) = -3$$, which of the following is TRUE?

Accepted Answer

$$f is a $$function.

Question 15

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

Accepted Answer

$$f is $$continuous at $$x = a.$$

Question 16

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

Accepted Answer

$$P(x) = 69 - \frac{1900}{x}$$

Question 17

If $$\lim_{x 	o 8} f(x) = f(8)$$, which of the following is TRUE?

Accepted Answer

$$f is $$continuous at $$x = 8.$$

Question 18

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

Accepted Answer

$$x = 1$$ and $$x = 7$$

Business Calculus: Functions, Limits, Derivatives, and Applications Study Guide

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