Question 1

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

Accepted Answer

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Question 2

In a free-fall experiment, an object is dropped from a height of 144 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   . Find the rate of change of the angle of elevation of the camera when   . Round your answer to four decimal places. ​   ​

Accepted Answer

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E)

Question 3

Find the rate of change of the distance D between the origin and a moving point on the graph of   if   centimeters per second. ​

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Question 4

An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider   and   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

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E)

Question 5

A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is   . ​
What is its velocity after 3 seconds?
​

Accepted Answer

A)  The velocity after 3 seconds is 229.3 meters per second. 
B)  The velocity after 3 seconds is -136.7 meters per second. 
C)  The velocity after 3 seconds is 92.6 meters per second. 
D)  The velocity after 3 seconds is 107.3 meters per second. 
E)  The velocity after 3 seconds is -151.4 meters per second 
A)  The velocity after 3 seconds is 229.3 meters per second. 
B)  The velocity after 3 seconds is -136.7 meters per second. 
C)  The velocity after 3 seconds is 92.6 meters per second. 
D)  The velocity after 3 seconds is 107.3 meters per second. 
E)  The velocity after 3 seconds is -151.4 meters per second

Question 6

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)  0.569 
B)  0.496 
C)  0.557 
D)  0.518 
E)  0.601 
A)  0.569 
B)  0.496 
C)  0.557 
D)  0.518 
E)  0.601

Question 7

Find   in terms of x and y given that   . ​

Accepted Answer

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Question 8

An airplane is flying in still air with an airspeed of 283 miles per hour. If it is climbing at an angle of 21°, find the rate at which it is gaining altitude. Round your answer to four decimal places. ​

Accepted Answer

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B)    
C)    
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D)    
E)

Question 9

Find the second derivative of the function   . ​

Accepted Answer

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E)

Question 10

Find the slope-intercept form of the equation of the line tangent to the graph of   when   . ​

Accepted Answer

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Question 11

Find   if   . ​

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Question 12

Find the derivative of the function   . ​

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Question 13

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

Accepted Answer

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Question 14

The displacement from equilibrium of an object in harmonic motion on the end of a spring is   where y is measured in feet and t is the time in seconds. Determine the velocity of the object when   . Round your answer to two decimal places. ​

Accepted Answer

A)  10.53 ft/sec 
B)  6.42 ft/sec 
C)  8.53 ft/sec 
D)  2.50 ft/sec 
E)  6.19 ft/sec 
A)  10.53 ft/sec 
B)  6.42 ft/sec 
C)  8.53 ft/sec 
D)  2.50 ft/sec 
E)  6.19 ft/sec

Question 15

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 16

Find the second derivative of the function   . ​

Accepted Answer

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

Question 17

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

Accepted Answer

A)  -0.493 
B)  0.451 
C)  -0.546 
D)  0.493 
E)  -0.444 
A)  -0.493 
B)  0.451 
C)  -0.546 
D)  0.493 
E)  -0.444

Question 18

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

Accepted Answer

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Question 19

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

Accepted Answer

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Question 20

Find the derivative of the function   . ​

Accepted Answer

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

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

Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second.

An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and 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.

A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is . What is its velocity after 3 seconds?

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 in terms of x and y given that .

An airplane is flying in still air with an airspeed of 283 miles per hour. If it is climbing at an angle of 21°, find the rate at which it is gaining altitude. Round your answer to four decimal places.

Find the second derivative of the function .

Find the slope-intercept form of the equation of the line tangent to the graph of when .

Find if .

Find the derivative of the function .

Find the derivative of the function . Simplify your answer.

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the velocity of the object when . Round your answer to two decimal places.

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

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

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

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

Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second. ​

An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and 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. ​ ​

A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is . ​ What is its velocity after 3 seconds? ​

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 in terms of x and y given that . ​

An airplane is flying in still air with an airspeed of 283 miles per hour. If it is climbing at an angle of 21°, find the rate at which it is gaining altitude. Round your answer to four decimal places. ​

Find the second derivative of the function . ​

Find the slope-intercept form of the equation of the line tangent to the graph of when . ​

Find if . ​

Find the derivative of the function . ​

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

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the velocity of the object when . Round your answer to two decimal places. ​

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

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

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

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

Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second.

An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and 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.

A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is . What is its velocity after 3 seconds?

Find in terms of x and y given that .

An airplane is flying in still air with an airspeed of 283 miles per hour. If it is climbing at an angle of 21°, find the rate at which it is gaining altitude. Round your answer to four decimal places.

Find the second derivative of the function .

Find the slope-intercept form of the equation of the line tangent to the graph of when .

Find if .

Find the derivative of the function .

Find the derivative of the function . Simplify your answer.

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the velocity of the object when . Round your answer to two decimal places.

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

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

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

Find the derivative of the function .