Question 1

​Find the derivative of the function   . ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 2

In a free-fall experiment,an object is dropped from a height of a = 256 feet.A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure.Assuming the object is released at time t = 0.At what time will the object reach the ground level? ​   ​

Accepted Answer

A) 3 seconds 
B) 6 seconds 
C) 7 seconds 
D) 5 seconds 
E) 4 seconds 
A) 3 seconds 
B) 6 seconds 
C) 7 seconds 
D) 5 seconds 
E) 4 seconds

Question 3

Find the derivative of the function   . ​

Accepted Answer

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

Question 4

Find the derivative of the function   using the limiting process. ​

Accepted Answer

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

Question 5

Find the derivative of the following function   using the limiting process. ​

Accepted Answer

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

Question 6

Apply Newton's Method to approximate the x-value of the indicated point of intersection of   and   .Continue the process until two successive approximations differ by less than 0.001.[Hint: Let   .] Round your answer to three decimal places. ​
​   ​

Accepted Answer

A) 5.494 
B) 8.725 
C) 6.494 
D) 7.725 
E) 4.641 
A) 5.494 
B) 8.725 
C) 6.494 
D) 7.725 
E) 4.641

Question 7

Find the slope of the tangent line   at the given point   .Round your answer to two decimal places if necessary. ​

Accepted Answer

A) 0.67 
B) 2 
C) 1 
D) 1.67 
E) 3 
A) 0.67 
B) 2 
C) 1 
D) 1.67 
E) 3

Question 8

​Find   for   . ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 9

Find the derivative of the function   .Simplify your answer. ​

Accepted Answer

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

Question 10

An airplane flies at an altitude of h = 6 miles towards a point directly over an observer.Consider θ and x as shown in the following figure.The speed of the plane is 400 miles per hour.Find   when   miles.Round your answer to three decimal places.   ​

Accepted Answer

A) -17.647   
B) 2.941   
C) 17.647   
D) 0.044   
E) -8.824   
A) -17.647   
B) 2.941   
C) 17.647   
D) 0.044   
E) -8.824

Question 11

The ordering and transportation cost C for the components used in manufacturing a product is   ,   where C is measured in thousands of dollars and x is the order size in hundreds.Find the rate of change of C with respect to x for   .Round your answer to two decimal places. ​

Accepted Answer

A) -23.65 thousand dollars per hundred 
B) 24.79 thousand dollars per hundred 
C) 11.85 thousand dollars per hundred 
D) -22.54 thousand dollars per hundred 
E) -34.28 thousand dollars per hundred 
A) -23.65 thousand dollars per hundred 
B) 24.79 thousand dollars per hundred 
C) 11.85 thousand dollars per hundred 
D) -22.54 thousand dollars per hundred 
E) -34.28 thousand dollars per hundred

Question 12

Find the derivative of the algebraic function   . ​

Accepted Answer

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

Question 13

A petrol car is parked 50 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 30 revolutions per minute.How fast is the light beam moving along the wall when the beam makes an angle of   with the perpendicular from the light to the wall.

Accepted Answer

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

Question 14

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 1368 feet tall.Find the time required for the coin to reach ground level.Round your answer to the three decimal places. ​

Accepted Answer

A) 3.082 sec 
B) 10.677 sec 
C) 11.152 sec 
D) 3.362 sec 
E) 10.523 sec 
A) 3.082 sec 
B) 10.677 sec 
C) 11.152 sec 
D) 3.362 sec 
E) 10.523 sec

Question 15

Find   by implicit differentiation. ​   ​

Accepted Answer

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

Question 16

Use Newton's Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places.Continue the process until two successive approximations differ by less than 0.001.[Hint: Let   .]

Accepted Answer

A) 2.651 
B) 2.703 
C) 2.660 
D) 2.764 
E) 2.600 
A) 2.651 
B) 2.703 
C) 2.660 
D) 2.764 
E) 2.600

Question 17

Find   by implicit differentiation. ​   ​

Accepted Answer

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

Question 18

An airplane is flying in still air with an airspeed of 266 miles per hour.If it is climbing at an angle of 22°,find the rate at which it is gaining altitude.Round your answer to four decimal places. ​

Accepted Answer

A) 112.4165   
B) 86.6011   
C) 120.7615   
D) 100.7692   
E) 99.6454   
A) 112.4165   
B) 86.6011   
C) 120.7615   
D) 100.7692   
E) 99.6454

Question 19

Find the derivative of the function   . ​

Accepted Answer

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

Question 20

A ladder a = 20 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 b = 4 feet per second.How fast is the top of the ladder moving down the wall when its base is 13 feet from the wall? Round your answer to two decimal places. ​   ​

Accepted Answer

A) 5.00   
B) -6.86   
C) -3.42   
D) 6.86   
E) -6.00   
A) 5.00   
B) -6.86   
C) -3.42   
D) 6.86   
E) -6.00

Find the derivative of the function .

In a free-fall experiment,an object is dropped from a height of a = 256 feet.A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure.Assuming the object is released at time t = 0.At what time will the object reach the ground level?

Find the derivative of the function .

Find the derivative of the function using the limiting process.

Find the derivative of the following function using the limiting process.

Apply Newton's Method to approximate the x-value of the indicated point of intersection of and .Continue the process until two successive approximations differ by less than 0.001.[Hint: Let .] Round your answer to three decimal places.

Find the slope of the tangent line at the given point .Round your answer to two decimal places if necessary.

Find for .

Find the derivative of the function .Simplify your answer.

An airplane flies at an altitude of h = 6 miles towards a point directly over an observer.Consider θ and x as shown in the following figure.The speed of the plane is 400 miles per hour.Find when miles.Round your answer to three decimal places.

The ordering and transportation cost C for the components used in manufacturing a product is , where C is measured in thousands of dollars and x is the order size in hundreds.Find the rate of change of C with respect to x for .Round your answer to two decimal places.

Find the derivative of the algebraic function .

A petrol car is parked 50 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 30 revolutions per minute.How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall.

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 1368 feet tall.Find the time required for the coin to reach ground level.Round your answer to the three decimal places.

Find by implicit differentiation.

Use Newton's Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places.Continue the process until two successive approximations differ by less than 0.001.[Hint: Let .]

Find by implicit differentiation.

An airplane is flying in still air with an airspeed of 266 miles per hour.If it is climbing at an angle of 22°,find the rate at which it is gaining altitude.Round your answer to four decimal places.

Find the derivative of the function .

A ladder a = 20 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 b = 4 feet per second.How fast is the top of the ladder moving down the wall when its base is 13 feet from the wall? Round your answer to two decimal places.

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 3: Differentiation

​Find the derivative of the function . ​

In a free-fall experiment,an object is dropped from a height of a = 256 feet.A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure.Assuming the object is released at time t = 0.At what time will the object reach the ground level? ​ ​

Find the derivative of the function . ​

Find the derivative of the function using the limiting process. ​

Find the derivative of the following function using the limiting process. ​

Apply Newton's Method to approximate the x-value of the indicated point of intersection of and .Continue the process until two successive approximations differ by less than 0.001.[Hint: Let .] Round your answer to three decimal places. ​ ​ ​

Find the slope of the tangent line at the given point .Round your answer to two decimal places if necessary. ​

​Find for . ​

Find the derivative of the function .Simplify your answer. ​

An airplane flies at an altitude of h = 6 miles towards a point directly over an observer.Consider θ and x as shown in the following figure.The speed of the plane is 400 miles per hour.Find when miles.Round your answer to three decimal places. ​

The ordering and transportation cost C for the components used in manufacturing a product is , where C is measured in thousands of dollars and x is the order size in hundreds.Find the rate of change of C with respect to x for .Round your answer to two decimal places. ​

Find the derivative of the algebraic function . ​

A petrol car is parked 50 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 30 revolutions per minute.How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall.

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 1368 feet tall.Find the time required for the coin to reach ground level.Round your answer to the three decimal places. ​

Find by implicit differentiation. ​ ​

Use Newton's Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places.Continue the process until two successive approximations differ by less than 0.001.[Hint: Let .]

Find by implicit differentiation. ​ ​

An airplane is flying in still air with an airspeed of 266 miles per hour.If it is climbing at an angle of 22°,find the rate at which it is gaining altitude.Round your answer to four decimal places. ​

Find the derivative of the function . ​

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find the derivative of the function .

In a free-fall experiment,an object is dropped from a height of a = 256 feet.A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure.Assuming the object is released at time t = 0.At what time will the object reach the ground level?

Find the derivative of the function .

Find the derivative of the function using the limiting process.

Find the derivative of the following function using the limiting process.

Apply Newton's Method to approximate the x-value of the indicated point of intersection of and .Continue the process until two successive approximations differ by less than 0.001.[Hint: Let .] Round your answer to three decimal places.

Find the slope of the tangent line at the given point .Round your answer to two decimal places if necessary.

Find for .

Find the derivative of the function .Simplify your answer.

An airplane flies at an altitude of h = 6 miles towards a point directly over an observer.Consider θ and x as shown in the following figure.The speed of the plane is 400 miles per hour.Find when miles.Round your answer to three decimal places.

The ordering and transportation cost C for the components used in manufacturing a product is , where C is measured in thousands of dollars and x is the order size in hundreds.Find the rate of change of C with respect to x for .Round your answer to two decimal places.

Find the derivative of the algebraic 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 1368 feet tall.Find the time required for the coin to reach ground level.Round your answer to the three decimal places.

Find by implicit differentiation.

Find by implicit differentiation.

An airplane is flying in still air with an airspeed of 266 miles per hour.If it is climbing at an angle of 22°,find the rate at which it is gaining altitude.Round your answer to four decimal places.

Find the derivative of the function .