Question 1

The graph of the function $f$ is shown above. Which of the following statements is false?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$ exists

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

The function $f$ is discontinuous at $x=4$ .

Answer

$\lim_{x o2}f\left(x
ight)$

Question 2

What is $f$ ?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

0

Answer

The limit does not exist.

Answer

1

Question 3

$\lim_{x o2}f\left(x
ight)$

Accepted Answer

-1

Answer

1

Answer

0

Answer

nonexistent

Question 4

$\lim_{x o2}f\left(x
ight)$

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 5

If $f$ , then find $x=4$ .

Accepted Answer

8

Answer

-1

Answer

2

Answer

0

Question 6

If $f$ , then find $x=4$ .

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 7

If $f$ , calculate $x=4$ .

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 8

Let $f$ be a function such that $x=4$ . Which of the following must be true?

I. $f$ is continuous at $x=3$ .

II. $f$ is differentiable at $x=3$ .

III. $f'$ is continuous at $x=3$ .

Accepted Answer

I and II only

Answer

II and III only

Answer

II only

Answer

I only

Question 9

What is the average value of $f$ on the interval [0, 2]?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 10

Let $f$ be the function given by $x=4$ . On which of the following intervals is the function $f$ decreasing?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 11

$\lim_{x o2}f\left(x
ight)$

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 12

A particle moves along the x-axis. The velocity of the particle at time t is $f$ . What is the total distance traveled by the particle from time $t=0$ to $t=2$ ?

Accepted Answer

16

Answer

18

Answer

13

Answer

10

Question 13

A tank contains 30 liters of water at time t = 5 hours. Water is being pumped into the tank at a rate of R(t) where R(t) is measured in liters per hour, and t is measured in hours. Selected values of R(t) are given in the table. Using a right Riemann sum with four subintervals and data from the table, what is the approximation of the number of liters of water that are in the tank at time t = 19 hours?

Accepted Answer

79

Answer

73.5

Answer

88

Answer

49

Question 14

Find the area between the curves $f$ and $x=4$ .

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 15

Let $f$ be the function defined by $x=4$ for all values of $f$ . Which of the following statements is true?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$ is continuous but not differentiable at $x=0$

Answer

$\lim_{x o2}f\left(x
ight)$ is not continuous at $x=0$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$ is differentiable at $x=0$

Question 16

Using the substitution $f$ , $x=4$ is equal to which of the following?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 17

If $f$ and $x=4$ , then find the derivative of $f$ at $t=0$ .

Accepted Answer

300

Answer

75

Answer

150

Answer

25

Question 18

The graph of a differentiable function $f$ is shown above. If $x=4$ , which of the following statement is true?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 19

A particle moves along the x-axis so that at any time $f$ its position is given by $x=4$ . For what values of $f$ the particle is at rest?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$ and $x=0$

Answer

$\lim_{x o2}f\left(x
ight)$ only

Answer

$\lim_{x o2}f\left(x
ight)$ only

Answer

$\lim_{x o2}f\left(x
ight)$ only

Question 20

The figure shows the graph of $f$ . If $x=4$ , which of the following could be the graph of $f$ ?

Accepted Answer

https://uploads.quizalize.com/4ea46a4d-17f1-428f-b076-30881eb446f3/question/7a89e85c940a02e6d9d383841757876b8a88de4b.jpeg

Answer

https://uploads.quizalize.com/4ea46a4d-17f1-428f-b076-30881eb446f3/question/325c89e3e93a31abed94020f74eab403784ebd80.jpeg

Answer

https://uploads.quizalize.com/4ea46a4d-17f1-428f-b076-30881eb446f3/question/7555f5d8d59aed33a49435f4eccd303d171c3b7a.jpeg

Answer

https://uploads.quizalize.com/4ea46a4d-17f1-428f-b076-30881eb446f3/question/971c929c17b2e8e87d32e3345de18f943405d140.jpeg

Question 21

The function $f$ is defined by $x=4$ . What point $f$ on the graph of $t=0$ has the property that the line tangent to $t=2$ at $\left(x,\ y\right)$ has a slope 0?

Accepted Answer

(-1, -1) only

Answer

(-1, -2) only

Answer

(0, 0) and (-1, -1)

Answer

(0, 0) only

Question 22

Let $f$ and let $x=4$ be the inverse of $f$ . Given that $t=0$ , what is the value of $t=2$ ?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

0

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

1

Question 23

If the graph of $f$ has a horizontal asymptote $x=4$ and a vertical asymptotes $f$ and $t=0$ , then find $t=2$ .

Accepted Answer

-1

Answer

-9

Answer

0

Answer

1

Question 24

What is the absolute minimum of the function $f$ given by $x=4$ ?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

0

Question 25

Let $f$ be a solution to the differential equation $x=4$ , where $f$ is a constant. The values of $t=0$ for selected values of $t=2$ are given in the table. Which of the following is an expression for $\left(x,\ y\right)$ ?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 26

Let $f$ be the function given by $x=4$ , where $f$ is a constant. For what value of $t=0$ does $t=2$ have critical points at $\left(x,\ y\right)$ ?

Accepted Answer

1

Answer

ln 1

Answer

0

Answer

-1

Question 27

Which of the following is the solution to the differential equation $f$ with the initial condition $x=4$ ?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 28

For $f$ , the position of a particle moving along the x-axis is given by $x=4$ . What is the acceleration of the particle at the point where the velocity is first equal to 0?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

-1

Answer

1

Answer

0

Question 29

If $f$ , what is the value of $x=4$ at the point (-1, 1)?

Accepted Answer

30

Answer

4

Answer

-4

Answer

0

Question 30

Let $f$ be the function given $x=4$ . For what value of $f$ is the slope of the line tangent to the graph of $t=0$ at $t=2$ equal to 1?

Accepted Answer

0.033

Answer

-0.578

Answer

0.097

Answer

0.028

Question 31

Let $f$ be a continuous function of the closed interval [-2, 7]. If f(-2)=-1 and f(7)=5, then the Intermediate Value Theorem guarantees that

Accepted Answer

$\lim_{x o2}f\left(x
ight)$ for at least one $x=0$ in the open interval (-2, 7).

Answer

$\lim_{x o2}f\left(x
ight)$ attains a maximum on the open interval (-2, 7).

Answer

$\lim_{x o2}f\left(x
ight)$ has at least one solution in the open interval (-2, 7).

Answer

$\lim_{x o2}f\left(x
ight)$

Question 32

The graph of $f$ crosses the x-axis at one point in the interval [6, 7]. What is the slope of the graph at this point?

Accepted Answer

0

Answer

-3.142

Answer

-6.283

Answer

3

Question 33

The function $f$ is defined on the closed interval [0, 9]. The graph of its derivative $x=4$ is shown. Which of the following statements must be true.

I. $f$ has six inflection points.

II. $f$ has a relative minimum at $f$ .

III. The graph of $f$ is concave down for $f'$

Accepted Answer

I and III only

Answer

I only

Answer

II only

Answer

III only

Question 34

Given the function defined by $f$ , find all values of $x=4$ for which the graph of $f$ is concave up.

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 35

If $f$ is a continuous function and if $x=4$ for all real numbers $f$ , then $t=0$

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 36

The graph of $f$ , the second derivative of $x=4$ , is shown above for $f$ . What are all intervals on which the graph of the function $t=0$ is concave down?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 37

If the base $f$ of a triangle is increasing at a rate of 2 centimeters per minute while its height $x=4$ is increasing at a rate of 2 centimeters per minute, which of the following must be true about the area $f$ of the triangle?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$ is always increasing

Answer

$\lim_{x o2}f\left(x
ight)$ is decreasing only when $x=0$

Answer

$\lim_{x o2}f\left(x
ight)$ is decreasing only when $x=0$

Answer

$\lim_{x o2}f\left(x
ight)$ is always decreasing

Question 38

A particle moves along a line so that its acceleration for $f$ is given by $x=4$ . If the particle's velocity at $f$ is -1, for what calue of $t=0$ will the velocity of the particle be zero?

Accepted Answer

0.88

Answer

0.78

Answer

-0.88

Answer

0.71

Question 39

Let $f$ be a function such that $x=4$ . Which of the following must be true?

Accepted Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Answer

$\lim_{x o2}f\left(x
ight)$

Question 40

Let $f$ be a polynomial function with values of $x=4$ at selected values of $f$ given in the table. Which of the following must be true for $t=0$

Accepted Answer

$\lim_{x o2}f\left(x
ight)$ has two inflection points

Answer

The range of $f$ is 7

Answer

$\lim_{x o2}f\left(x
ight)$ is concave down

Answer

$\lim_{x o2}f\left(x
ight)$ has at least two critical points

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