Question 1

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 2

Find the slope of the graph of the function at the given value.   when

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 3

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.

Accepted Answer

A)  2.849 sec 
B)  10.273 sec 
C)  10.693 sec 
D)  3.087 sec 
E)  10.091 sec 
A)  2.849 sec 
B)  10.273 sec 
C)  10.693 sec 
D)  3.087 sec 
E)  10.091 sec C

Question 4

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

A ball is thrown straight down from the top of a 300-ft building with an initial velocity of -12 ft per second. The position function is   . What is the velocity of the ball after 4 seconds?

Accepted Answer

A)  The velocity after 4 seconds is -76 ft per second. 
B)  The velocity after 4 seconds is -116 ft per second. 
C)  The velocity after 4 seconds is -140 ft per second. 
D)  The velocity after 4 seconds is -52 ft per second. 
E)  The velocity after 4 seconds is -280 ft per second. 
A)  The velocity after 4 seconds is -76 ft per second. 
B)  The velocity after 4 seconds is -116 ft per second. 
C)  The velocity after 4 seconds is -140 ft per second. 
D)  The velocity after 4 seconds is -52 ft per second. 
E)  The velocity after 4 seconds is -280 ft per second.

Question 6

Find the slope of the graph of the function at the given value.   when

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1372 feet tall. Determine the average velocity of the coin over the time interval   .

Accepted Answer

A)  -113 ft/sec 
B)  80 ft/sec 
C)  112 ft/sec 
D)  -112 ft/sec 
E)  -80 ft/sec 
A)  -113 ft/sec 
B)  80 ft/sec 
C)  112 ft/sec 
D)  -112 ft/sec 
E)  -80 ft/sec

Question 8

Find the slope-intercept equation of the line tangent to the graph of   when

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.

Accepted Answer

A)  -286.705 ft/sec 
B)  -138.492 ft/sec 
C)  -111.041 ft/sec 
D)  -276.984 ft/sec 
E)  -261.984 ft/sec 
A)  -286.705 ft/sec 
B)  -138.492 ft/sec 
C)  -111.041 ft/sec 
D)  -276.984 ft/sec 
E)  -261.984 ft/sec

Question 10

Use the rules of differentiation to find the derivative of the function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1370 feet tall. Determine the velocity function for the coin.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the instantaneous velocity of the coin when   .

Accepted Answer

A)  -96 ft/sec 
B)  -32 ft/sec 
C)  -20 ft/sec 
D)  -144 ft/sec 
E)  -48 ft/sec 
A)  -96 ft/sec 
B)  -32 ft/sec 
C)  -20 ft/sec 
D)  -144 ft/sec 
E)  -48 ft/sec

Question 13

Find the slope of the graph of the function at the given value.   when

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

A projectile is shot upwards from the surface of the earth with an initial velocity of 108 meters per second. The position function is   . What is its velocity after 7 seconds?

Accepted Answer

A)  The velocity after 7 seconds is 181.7 meters per second. 
B)  The velocity after 7 seconds is -142.3 meters per second. 
C)  The velocity after 7 seconds is 39.4 meters per second. 
D)  The velocity after 7 seconds is 73.7 meters per second. 
E)  The velocity after 7 seconds is -176.6 meters per second. 
A)  The velocity after 7 seconds is 181.7 meters per second. 
B)  The velocity after 7 seconds is -142.3 meters per second. 
C)  The velocity after 7 seconds is 39.4 meters per second. 
D)  The velocity after 7 seconds is 73.7 meters per second. 
E)  The velocity after 7 seconds is -176.6 meters per second.

Question 15

Find the slope of the graph of the function at the given value.   at

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Determine all values of   , (if any), at which the graph of the function has a horizontal tangent.

Accepted Answer

A)    
B)    
C)    
D)    
E)  The graph has no horizontal tangents. 
A)    
B)    
C)    
D)    
E)  The graph has no horizontal tangents.

Question 17

The volume of a cube with sides of length s is given by   . Find the rate of change of volume with respect to   when   centimeters.

Accepted Answer

A)  648 cm2 
B)  216 cm2 
C)  36 cm2 
D)  108 cm2 
E)  72 cm2 
A)  648 cm2 
B)  216 cm2 
C)  36 cm2 
D)  108 cm2 
E)  72 cm2

Question 18

Find the derivative of the function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the derivative of the function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Find the derivative of the function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Exam 3: Section 2: Differentiation

Find the derivative of the function.

Find the slope of the graph of the function at the given value. when

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.

Find the derivative of the function.

A ball is thrown straight down from the top of a 300-ft building with an initial velocity of -12 ft per second. The position function is . What is the velocity of the ball after 4 seconds?

Find the slope of the graph of the function at the given value. when

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1372 feet tall. Determine the average velocity of the coin over the time interval .

Find the slope-intercept equation of the line tangent to the graph of when

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.

Use the rules of differentiation to find the derivative of the function .

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1370 feet tall. Determine the velocity function for the coin.

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the instantaneous velocity of the coin when .

Find the slope of the graph of the function at the given value. when

A projectile is shot upwards from the surface of the earth with an initial velocity of 108 meters per second. The position function is . What is its velocity after 7 seconds?

Find the slope of the graph of the function at the given value. at

Determine all values of , (if any), at which the graph of the function has a horizontal tangent.

The volume of a cube with sides of length s is given by . Find the rate of change of volume with respect to when centimeters.

Find the derivative of the function .

Find the derivative of the function .

Find the derivative of the function .

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series