Question 1

Find the second derivative of the function   . ​

Accepted Answer

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

Question 2

Complete two iterations of Newton's Method to approximate a zero of the function using the given initial guess. What is the value of   of such an approximation? Round your answer to 5 decimal places. ​   ,   ​

Accepted Answer

A)  85.42370 
B)  78.37037 
C)  86.20741 
D)  86.99111 
A)  85.42370 
B)  78.37037 
C)  86.20741 
D)  86.99111 B

Question 3

Find an equation of the tangent line to the graph of   at the point   . ​

Accepted Answer

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

Question 4

A petrol car is parked 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   as a function of x. ​   ​

Accepted Answer

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

Question 5

Use the alternative form of the derivative to find the derivative of the function   at   . ​

Accepted Answer

A)    
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

Differentiate the function   . ​

Accepted Answer

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

Question 8

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

Accepted Answer

A)  0.250 
B)  -0.250 
C)  -0.292 
D)  0.281 
E)  0.197 
A)  0.250 
B)  -0.250 
C)  -0.292 
D)  0.281 
E)  0.197

Question 9

Use the Product Rule to differentiate   . ​

Accepted Answer

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

Question 10

A ladder 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 2 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)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Find the slope   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 12

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 13

Find   by implicit differentiation. ​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find the derivative of the function   by the limit process. ​

Accepted Answer

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

Question 16

Identify the graph which has the following characteristics.       ​ 
Graph 1
  ​
Graph 2
​  ​
Graph 3
​  
Graph 4
​   ​

Accepted Answer

A)  Graph 3 
B)  Graph 4 
C)  Graph 2 
D)  Graph 1 
E)  none of the above 
A)  Graph 3 
B)  Graph 4 
C)  Graph 2 
D)  Graph 1 
E)  none of the above

Question 17

Use implicit differentiation to find   . ​   ​

Accepted Answer

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

Question 18

Approximate the positive zero(s) of the function   to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. ​

Accepted Answer

A)  -1.207 
B)  1.105 
C)  1.082 
D)  -1.105 
E)  1.156 
A)  -1.207 
B)  1.105 
C)  1.082 
D)  -1.105 
E)  1.156

Question 19

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing? ​   ​

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)

Find the second derivative of the function .

Complete two iterations of Newton's Method to approximate a zero of the function using the given initial guess. What is the value of of such an approximation? Round your answer to 5 decimal places. ,

Find an equation of the tangent line to the graph of at the point .

A petrol car is parked 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 as a function of x.

Use the alternative form of the derivative to find the derivative of the function at .

Find the derivative of the function .

Differentiate the function .

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

Use the Product Rule to differentiate .

A ladder 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 2 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.

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

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

Find by implicit differentiation.

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

Find the derivative of the function by the limit process.

Identify the graph which has the following characteristics. Graph 1 Graph 2 Graph 3 Graph 4

Use implicit differentiation to find .

Approximate the positive zero(s) of the function to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing?

Find the derivative of the function.

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 3: Differentiation

Find the second derivative of the function . ​

Complete two iterations of Newton's Method to approximate a zero of the function using the given initial guess. What is the value of of such an approximation? Round your answer to 5 decimal places. ​ , ​

Find an equation of the tangent line to the graph of at the point . ​

A petrol car is parked 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 as a function of x. ​ ​

Use the alternative form of the derivative to find the derivative of the function at . ​

Find the derivative of the function . ​

Differentiate the function . ​

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

Use the Product Rule to differentiate . ​

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

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

Find by implicit differentiation. ​ ​

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

Find the derivative of the function by the limit process. ​

Identify the graph which has the following characteristics. ​ Graph 1 ​ Graph 2 ​ ​ Graph 3 ​ Graph 4 ​ ​

Use implicit differentiation to find . ​ ​

Approximate the positive zero(s) of the function to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. ​

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing? ​ ​

Find the derivative of the function. ​ ​

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find the second derivative of the function .

Complete two iterations of Newton's Method to approximate a zero of the function using the given initial guess. What is the value of of such an approximation? Round your answer to 5 decimal places. ,

Find an equation of the tangent line to the graph of at the point .

A petrol car is parked 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 as a function of x.

Use the alternative form of the derivative to find the derivative of the function at .

Find the derivative of the function .

Differentiate the function .

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

Use the Product Rule to differentiate .

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

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

Find by implicit differentiation.

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

Find the derivative of the function by the limit process.

Identify the graph which has the following characteristics. Graph 1 Graph 2 Graph 3 Graph 4

Use implicit differentiation to find .

Approximate the positive zero(s) of the function to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing?

Find the derivative of the function.