Question 1

Find   by implicit differentiation given that   . ​

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Use implicit differentiation to find   . ​   ​

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Complete two iterations of Newton's Method for the function   using the initial guess   .Round all numerical values in your answer to four decimal places. ​

Accepted Answer

A) ​
 
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1

2

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B) ​

1

2

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C) ​

1

2

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D) ​

1

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E) ​

1

2

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A) ​
 
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1

2

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B) ​

1

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C) ​

1

2

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D) ​

1

2

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E) ​

1

2

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Question 6

Find   by implicit differentiation given that   .Use the original equation to simplify your answer. ​

Accepted Answer

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

Question 7

Approximate the fixed point of the function   between   and   to two decimal places.[A fixed point   of a function f is a value of x such that   .] ​

Accepted Answer

A) 0.65 
B) 0 
C) 0.74 
D) 1.00 
E) 0.91 
A) 0.65 
B) 0 
C) 0.74 
D) 1.00 
E) 0.91

Question 8

A petrol car is parked ​a​ = 40 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 30 revolutions per minute.Write θ as a function of x. ​   ​

Accepted Answer

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

Question 9

Differentiate   with respect to t (x and y are functions of t). ​

Accepted Answer

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

Question 10

An isosceles triangle is inscribed in a semicircle,as shown in the diagram,and it continues to be inscribed as the semicircle changes size.The area of the semicircle is increasing at the rate of 1 cmS1U1P12S1S1P0/sec when the radius of the semicircle is 6 cm.
​  
-​How fast is the radius of the semicircle increasing when the radius is 6 cm? Include units in your answer.​ Round your answer to 3 decimal places.

Accepted Answer

The answer of An isosceles triangle is inscribed in a...

Question 11

Suppose that the total number of arrests T (in thousands)for all males ages 14 to 27 in 2006 is approximated by the model   where x is the age in years (see figure).Approximate the two ages to one decimal place that had total arrests of 300 thousand. ​   ​

Accepted Answer

A) 16.1;22.9 
B) 17.4;21.3 
C) 15.1;25.9 
D) 16.1;25.9 
E) 15.1;21.3 
A) 16.1;22.9 
B) 17.4;21.3 
C) 15.1;25.9 
D) 16.1;25.9 
E) 15.1;21.3

Question 12

The radius of a right circular cylinder is   and its height is   ,where t is time in seconds and the dimensions are in inches.Find the rate of change of the volume of the cylinder,V,with respect to time. ​

Accepted Answer

A)    cubic inches per second 
B)    cubic inches per second 
C)    cubic inches per second 
D)    cubic inches per second 
E)    cubic inches per second 
A)    cubic inches per second 
B)    cubic inches per second 
C)    cubic inches per second 
D)    cubic inches per second 
E)    cubic inches per second

Question 13

Evaluate   for the equation   at the given point   .Round your answer to two decimal places if necessary. ​

Accepted Answer

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

Question 14

A conical tank (with vertex down)is 20 feet across the top and 18 feet deep.If water is flowing into the tank at a rate of 20 cubic feet per minute,find the rate of change of the depth of the water when the water is 12 feet deep. ​

Accepted Answer

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

Question 15

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) 0.444 
B) 0.371 
C) 0.432 
D) 0.393 
E) 0.476 
A) 0.444 
B) 0.371 
C) 0.432 
D) 0.393 
E) 0.476

Question 16

Find the derivative of the function   . ​

Accepted Answer

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

Question 17

A population of 420 bacteria is introduced into a culture and grows in number according to the equation   where t is measured in hours.Find the rate at which the population is growing when   .Round your answer to two decimal places. ​

Accepted Answer

A) 119.45 bacteria per hour 
B) 41.31 bacteria per hour 
C) 31.11 bacteria per hour 
D) 11.91 bacteria per hour 
E) 34.54 bacteria per hour 
A) 119.45 bacteria per hour 
B) 41.31 bacteria per hour 
C) 31.11 bacteria per hour 
D) 11.91 bacteria per hour 
E) 34.54 bacteria per hour

Question 18

Differentiate the function   . ​

Accepted Answer

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

Question 19

Find   by implicit differentiation. ​   ​

Accepted Answer

A)    
B)    
A)    
B)

Question 20

Find   in terms of x and y given that   .Use the original equation to simplify your answer. ​

Accepted Answer

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

Find by implicit differentiation given that .

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

Use implicit differentiation to find .

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

Complete two iterations of Newton's Method for the function using the initial guess .Round all numerical values in your answer to four decimal places.

Find by implicit differentiation given that .Use the original equation to simplify your answer.

Approximate the fixed point of the function between and to two decimal places.[A fixed point of a function f is a value of x such that .]

A petrol car is parked a = 40 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 30 revolutions per minute.Write θ as a function of x.

Differentiate with respect to t (x and y are functions of t).

Suppose that the total number of arrests T (in thousands)for all males ages 14 to 27 in 2006 is approximated by the model where x is the age in years (see figure).Approximate the two ages to one decimal place that had total arrests of 300 thousand.

The radius of a right circular cylinder is and its height is ,where t is time in seconds and the dimensions are in inches.Find the rate of change of the volume of the cylinder,V,with respect to time.

Evaluate for the equation at the given point .Round your answer to two decimal places if necessary.

A conical tank (with vertex down)is 20 feet across the top and 18 feet deep.If water is flowing into the tank at a rate of 20 cubic feet per minute,find the rate of change of the depth of the water when the water is 12 feet deep.

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 the derivative of the function .

A population of 420 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours.Find the rate at which the population is growing when .Round your answer to two decimal places.

Differentiate the function .

Find by implicit differentiation.

Find in terms of x and y given that .Use the original equation to simplify your answer.

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 by implicit differentiation given that . ​

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

Use implicit differentiation to find . ​ ​

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

Complete two iterations of Newton's Method for the function using the initial guess .Round all numerical values in your answer to four decimal places. ​

Find by implicit differentiation given that .Use the original equation to simplify your answer. ​

Approximate the fixed point of the function between and to two decimal places.[A fixed point of a function f is a value of x such that .] ​

A petrol car is parked ​a​ = 40 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 30 revolutions per minute.Write θ as a function of x. ​ ​

Differentiate with respect to t (x and y are functions of t). ​

Suppose that the total number of arrests T (in thousands)for all males ages 14 to 27 in 2006 is approximated by the model where x is the age in years (see figure).Approximate the two ages to one decimal place that had total arrests of 300 thousand. ​ ​

The radius of a right circular cylinder is and its height is ,where t is time in seconds and the dimensions are in inches.Find the rate of change of the volume of the cylinder,V,with respect to time. ​

Evaluate for the equation at the given point .Round your answer to two decimal places if necessary. ​

A conical tank (with vertex down)is 20 feet across the top and 18 feet deep.If water is flowing into the tank at a rate of 20 cubic feet per minute,find the rate of change of the depth of the water when the water is 12 feet deep. ​

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 the derivative of the function . ​

A population of 420 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours.Find the rate at which the population is growing when .Round your answer to two decimal places. ​

Differentiate the function . ​

Find by implicit differentiation. ​ ​

Find in terms of x and y given that .Use the original equation to simplify your answer. ​

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 by implicit differentiation given that .

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

Use implicit differentiation to find .

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

Complete two iterations of Newton's Method for the function using the initial guess .Round all numerical values in your answer to four decimal places.

Find by implicit differentiation given that .Use the original equation to simplify your answer.

Approximate the fixed point of the function between and to two decimal places.[A fixed point of a function f is a value of x such that .]

A petrol car is parked a = 40 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 30 revolutions per minute.Write θ as a function of x.

Differentiate with respect to t (x and y are functions of t).

Suppose that the total number of arrests T (in thousands)for all males ages 14 to 27 in 2006 is approximated by the model where x is the age in years (see figure).Approximate the two ages to one decimal place that had total arrests of 300 thousand.

The radius of a right circular cylinder is and its height is ,where t is time in seconds and the dimensions are in inches.Find the rate of change of the volume of the cylinder,V,with respect to time.

Evaluate for the equation at the given point .Round your answer to two decimal places if necessary.

A conical tank (with vertex down)is 20 feet across the top and 18 feet deep.If water is flowing into the tank at a rate of 20 cubic feet per minute,find the rate of change of the depth of the water when the water is 12 feet deep.

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 the derivative of the function .

A population of 420 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours.Find the rate at which the population is growing when .Round your answer to two decimal places.

Differentiate the function .

Find by implicit differentiation.

Find in terms of x and y given that .Use the original equation to simplify your answer.