Question 1

The radius r of a sphere is increasing at a rate of   inches per minute. Find the rate of change of the volume when r =   inches.

Accepted Answer

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

Question 2

A ladder   feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of   feet per second. How fast is the top of the ladder moving down the wall when its base is   feet from the wall? Round your answer to two decimal places.

Accepted Answer

A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec 
A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec C

Question 3

A ladder   feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of   feet per second. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changed when the base of the ladder is   feet from the wall. Round your answer to two decimal places.

Accepted Answer

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

Question 4

A ladder   feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of   feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is   feet from the wall. Round your answer to three decimal places.

Accepted Answer

A)    rad/sec 
B)    rad/sec 
C)    rad/sec 
D)    rad/sec 
E)    rad/sec 
A)    rad/sec 
B)    rad/sec 
C)    rad/sec 
D)    rad/sec 
E)    rad/sec

Question 5

A conical tank (with vertex down) is   feet across the top and   feet deep. If water is flowing into the tank at a rate of   cubic feet per minute, find the rate of change of the depth of the water when the water is   feet deep.

Accepted Answer

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

Question 6

A spherical balloon is inflated with gas at the rate of   cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is   centimeters?

Accepted Answer

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

Question 7

All edges of a cube are expanding at a rate of   centimeters per second. How fast is the volume changing when each edge is   centimeters?

Accepted Answer

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

Question 8

Assume that x and y are both differentiable functions of t. Find   for the equation   .

Accepted Answer

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

Question 9

A point is moving along the graph of the function   such that   =   centimeters per second. Find   when   .

Accepted Answer

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

Question 10

A point is moving along the graph of the function   such that   centimeters per second. Find   when x =   .

Accepted Answer

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

Question 11

A man 6 feet tall walks at a rate of   feet per second away from a light that is 15 feet above the ground (see figure). When he is   feet from the base of the light, at what rate is the length of his shadow changing?

Accepted Answer

A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec 
A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec

Question 12

The radius, r, of a circle is decreasing at a rate of   centimeters per minute. Find the rate of change of area, A, when the radius is   .

Accepted Answer

A)    sq cm/min 
B)    sq cm/min 
C)    sq cm/min 
D)    sq cm/min 
E)    sq cm/min 
A)    sq cm/min 
B)    sq cm/min 
C)    sq cm/min 
D)    sq cm/min 
E)    sq cm/min

Question 13

An airplane is flying in still air with an airspeed of   miles per hour. If it is climbing at an angle of   , find the rate at which it is gaining altitude. Round your answer to four decimal places.

Accepted Answer

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

Question 14

A man 6 feet tall walks at a rate of   feet per second away from a light that is 15 feet above the ground (see figure). When he is   feet from the base of the light, at what rate is the tip of his shadow moving?

Accepted Answer

A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec 
A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec

Question 15

Assume that x and y are both differentiable functions of t . Find   for the equation   .

Accepted Answer

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

Question 16

Find the rate of change of the distance   between the origin and a moving point on the graph of   if   centimeters per second.

Accepted Answer

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

Exam 3: Section 7: Differentiation

The radius r of a sphere is increasing at a rate of inches per minute. Find the rate of change of the volume when r = inches.

A ladder feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of feet per second. How fast is the top of the ladder moving down the wall when its base is feet from the wall? Round your answer to two decimal places.

A conical tank (with vertex down) is feet across the top and feet deep. If water is flowing into the tank at a rate of cubic feet per minute, find the rate of change of the depth of the water when the water is feet deep.

A spherical balloon is inflated with gas at the rate of cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is centimeters?

All edges of a cube are expanding at a rate of centimeters per second. How fast is the volume changing when each edge is centimeters?

Assume that x and y are both differentiable functions of t. Find for the equation .

A point is moving along the graph of the function such that = centimeters per second. Find when .

A point is moving along the graph of the function such that centimeters per second. Find when x = .

A man 6 feet tall walks at a rate of feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the length of his shadow changing?

The radius, r, of a circle is decreasing at a rate of centimeters per minute. Find the rate of change of area, A, when the radius is .

An airplane is flying in still air with an airspeed of miles per hour. If it is climbing at an angle of , find the rate at which it is gaining altitude. Round your answer to four decimal places.

A man 6 feet tall walks at a rate of feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the tip of his shadow moving?

Assume that x and y are both differentiable functions of t . Find for the equation .

Find the rate of change of the distance between the origin and a moving point on the graph of if centimeters per second.

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 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: 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

Section 5: Infinite Series

Section 6: Infinite Series

Section 7: Infinite Series

Section 8: Infinite Series

Section 9: Infinite Series

Section 10: Infinite Series