Question 1

Find the slope m of the line tangent to the graph of the function   at the point   . ​

Accepted Answer

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

Question 2

Use the Product Rule to differentiate   . ​

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 5

Find an equation of the tangent line to the graph of the function   at the point   .The coefficients below are given to two decimal places. ​

Accepted Answer

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

Question 6

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 7

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 8

Find the derivative of the function   . ​

Accepted Answer

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

Question 9

Find an equation of the line that is tangent to the graph of the function   and parallel to the line   . ​

Accepted Answer

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

Question 10

Suppose a 27-centimeter pendulum moves according to the equation   where θ is the angular displacement from the vertical in radians and t is the time in seconds.Determine the rate of change of θ when t = 7 seconds.Round your answer to four decimal places. ​

Accepted Answer

A) 2.9207 radians per second 
B) 4.0358 radians per second 
C) 0.6416 radians per second 
D) 2.7593 radians per second 
E) 5.4991 radians per second 
A) 2.9207 radians per second 
B) 4.0358 radians per second 
C) 0.6416 radians per second 
D) 2.7593 radians per second 
E) 5.4991 radians per second

Question 11

​What does the limit statement   represent? ​

Accepted Answer

A) ​0 
B) ​   
C) ​   ,if
  
D) ​6 
A) ​0 
B) ​   
C) ​   ,if
  
D) ​6

Question 12

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

Accepted Answer

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

Question 13

​If   ,   and   ,what is the equation of the tangent line to   at   ? ​

Accepted Answer

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

Question 14

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

The radius,r,of a circle is increasing at a rate of 3 centimeters per minute.​Find the rate of change of area,A,when the radius is 6. ​

Accepted Answer

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

Question 17

Find the second derivative of the function   . ​

Accepted Answer

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

Question 18

Use Newton's Method to approximate the zero(s)of the function   accurate to three decimal places. ​

Accepted Answer

A) 0.486 
B) -0.486 
C) -0.528 
D) 0.517 
E) 0.433 
A) 0.486 
B) -0.486 
C) -0.528 
D) 0.517 
E) 0.433

Question 19

Use logarithmic differentiation to find   . ​   ​

Accepted Answer

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

Question 20

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

Accepted Answer

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

Find the slope m of the line tangent to the graph of the function at the point .

Use the Product Rule to differentiate .

Find the derivative of the function .Simplify your answer.

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

Find an equation of the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places.

Find the derivative of the function.

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

Find the derivative of the function .

Find an equation of the line that is tangent to the graph of the function and parallel to the line .

Suppose a 27-centimeter pendulum moves according to the equation where θ is the angular displacement from the vertical in radians and t is the time in seconds.Determine the rate of change of θ when t = 7 seconds.Round your answer to four decimal places.

What does the limit statement represent?

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

If , and ,what is the equation of the tangent line to at ?

Find the derivative of the function.

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

The radius,r,of a circle is increasing at a rate of 3 centimeters per minute.Find the rate of change of area,A,when the radius is 6.

Find the second derivative of the function .

Use Newton's Method to approximate the zero(s)of the function accurate to three decimal places.

Use logarithmic differentiation to find .

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

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 slope m of the line tangent to the graph of the function at the point . ​

Use the Product Rule to differentiate . ​

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

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

Find an equation of the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places. ​

Find the derivative of the function. ​ ​

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

Find the derivative of the function . ​

Find an equation of the line that is tangent to the graph of the function and parallel to the line . ​

Suppose a 27-centimeter pendulum moves according to the equation where θ is the angular displacement from the vertical in radians and t is the time in seconds.Determine the rate of change of θ when t = 7 seconds.Round your answer to four decimal places. ​

​What does the limit statement represent? ​

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

​If , and ,what is the equation of the tangent line to at ? ​

Find the derivative of the function. ​ ​

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

The radius,r,of a circle is increasing at a rate of 3 centimeters per minute.​Find the rate of change of area,A,when the radius is 6. ​

Find the second derivative of the function . ​

Use Newton's Method to approximate the zero(s)of the function accurate to three decimal places. ​

Use logarithmic differentiation to find . ​ ​

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

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 slope m of the line tangent to the graph of the function at the point .

Use the Product Rule to differentiate .

Find the derivative of the function .Simplify your answer.

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

Find an equation of the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places.

Find the derivative of the function.

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

Find the derivative of the function .

Find an equation of the line that is tangent to the graph of the function and parallel to the line .

Suppose a 27-centimeter pendulum moves according to the equation where θ is the angular displacement from the vertical in radians and t is the time in seconds.Determine the rate of change of θ when t = 7 seconds.Round your answer to four decimal places.

What does the limit statement represent?

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

If , and ,what is the equation of the tangent line to at ?

Find the derivative of the function.

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

The radius,r,of a circle is increasing at a rate of 3 centimeters per minute.Find the rate of change of area,A,when the radius is 6.

Find the second derivative of the function .

Use Newton's Method to approximate the zero(s)of the function accurate to three decimal places.

Use logarithmic differentiation to find .

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