Question 1

Use the Product Rule to differentiate. ​   ​

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Question 2

Find the derivative of the function   . ​

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Question 3

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

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Question 4

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

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Question 5

Find the derivative of the function   . ​

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Question 6

Use the Product Rule to differentiate   . ​

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Question 7

Find the derivative of the function. ​   ​

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Question 8

Find   in terms of x and y. ​   ​

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Question 9

Use the quotient rule to differentiate the following function   and evaluate   . ​

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Question 10

Find the second derivative of the function   . ​

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Question 11

Complete two iterations of Newton's Method for the function   using the initial guess 0.8.Round your answers to four decimal places. ​

Accepted Answer

A) 1.0251,1.0001 
B) 1.0251,1.0005 
C) 1.0251,1.0004 
D) 1.0248,1.0002 
E) 1.0250,1.0003 
A) 1.0251,1.0001 
B) 1.0251,1.0005 
C) 1.0251,1.0004 
D) 1.0248,1.0002 
E) 1.0250,1.0003

Question 12

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 1364 feet tall.Determine the average velocity of the coin over the time interval   . ​

Accepted Answer

A) -49   
B) 15   
C) 45   
D) -45   
E) -15   
A) -49   
B) 15   
C) 45   
D) -45   
E) -15

Question 13

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

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Question 14

Evaluate the derivative of the function at the given point. ​   ,

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Question 15

Find the slope of the graph of the function at the given value. ​   when   ​

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Question 16

​In right triangle   ,point   is moving along a leg of the right triangle toward point   at a rate of   cm/sec and point   is moving toward point   at a rate of   cm/sec along a line containing the other leg of the right triangle,as illustrated in the triangle shown below.What is the rate of change in the area of   ,with respect to time,at the instant when   cm and   cm? ​   ​

Accepted Answer

A) -4.48 cm2/sec 
B) -3.36 cm2/sec 
C) -3.2 cm2/sec 
D) ​​-4 cm2/sec 
A) -4.48 cm2/sec 
B) -3.36 cm2/sec 
C) -3.2 cm2/sec 
D) ​​-4 cm2/sec

Question 17

​Find   if   . ​

Accepted Answer

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

Question 18

​Find the second derivative of   if   . ​

Accepted Answer

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Question 19

Use logarithmic differentiation to find the derivative of   . ​

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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.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 19 feet from the wall.Round your answer to three decimal places. ​   ​​

Accepted Answer

A) 0.528   
B) 0.641   
C) 4.058   
D) 7.604   
E) 0.339   
A) 0.528   
B) 0.641   
C) 4.058   
D) 7.604   
E) 0.339

Use the Product Rule to differentiate.

Find the derivative of the function .

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

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

Find the derivative of the function .

Use the Product Rule to differentiate .

Find the derivative of the function.

Find in terms of x and y.

Use the quotient rule to differentiate the following function and evaluate .

Find the second derivative of the function .

Complete two iterations of Newton's Method for the function using the initial guess 0.8.Round your answers to four decimal places.

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 1364 feet tall.Determine the average velocity of the coin over the time interval .

Find the derivative of the function by the limit process.

Evaluate the derivative of the function at the given point. ,

Find the slope of the graph of the function at the given value. when

Find if .

Find the second derivative of if .

Use logarithmic differentiation to find the derivative of .

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

Use the Product Rule to differentiate. ​ ​

Find the derivative of the function . ​

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

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

Find the derivative of the function . ​

Use the Product Rule to differentiate . ​

Find the derivative of the function. ​ ​

Find in terms of x and y. ​ ​

Use the quotient rule to differentiate the following function and evaluate . ​

Find the second derivative of the function . ​

Complete two iterations of Newton's Method for the function using the initial guess 0.8.Round your answers to four decimal places. ​

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 1364 feet tall.Determine the average velocity of the coin over the time interval . ​

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

Evaluate the derivative of the function at the given point. ​ ,

Find the slope of the graph of the function at the given value. ​ when ​

​Find if . ​

​Find the second derivative of if . ​

Use logarithmic differentiation to find the derivative of . ​

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

Use the Product Rule to differentiate.

Find the derivative of the function .

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

Find the derivative of the function .

Use the Product Rule to differentiate .

Find the derivative of the function.

Find in terms of x and y.

Use the quotient rule to differentiate the following function and evaluate .

Find the second derivative of the function .

Complete two iterations of Newton's Method for the function using the initial guess 0.8.Round your answers to four decimal places.

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 1364 feet tall.Determine the average velocity of the coin over the time interval .

Find the derivative of the function by the limit process.

Evaluate the derivative of the function at the given point. ,

Find the slope of the graph of the function at the given value. when

Find if .

Find the second derivative of if .

Use logarithmic differentiation to find the derivative of .