Question 1

A point is moving along the graph of the function   such that   centimeters per second. Find   when   . ​

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Question 2

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

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Question 3

Differentiate the function   . ​

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Question 4

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

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Question 5

Find   by implicit differentiation. ​   .
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Question 6

The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute. ​
Find the rate of change of area, A, when the radius is 3.
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Question 7

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 1,366 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places. ​

Accepted Answer

A)  2.464 sec 
B)  9.543 sec 
C)  9.878 sec 
D)  2.640 sec 
E)  9.320 sec 
A)  2.464 sec 
B)  9.543 sec 
C)  9.878 sec 
D)  2.640 sec 
E)  9.320 sec

Question 8

Find   by implicit differentiation. ​   ​

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Question 9

Differentiate the function   . ​

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Question 10

Find   if   . ​

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Question 11

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of   with the perpendicular from the light to the wall.   ​

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Question 12

Find the derivative of the function   . ​

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Question 13

Find   by implicit differentiation. ​   ​

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Question 14

Evaluate the derivative of the function   at the point   . ​

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Question 15

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 1,372 feet tall. Determine the velocity function for the coin. ​

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Question 16

Find   by implicit differentiation. ​   ​

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Question 17

Find the derivative of the function   . ​

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Question 18

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Round your answer to 5 decimal places. ​   ,   ​

Accepted Answer

A)  0.86641 
B)  0.89724 
C)  0.86547 
D)  1.07000 
A)  0.86641 
B)  0.89724 
C)  0.86547 
D)  1.07000

Question 19

A ball is thrown straight down from the top of a 220-ft building with an initial velocity of -16 ft per second. The position function is   . What is the velocity of the ball after 4 seconds? ​

Accepted Answer

A)  The velocity after 4 seconds is -80 ft per second. 
B)  The velocity after 4 seconds is -112 ft per second. 
C)  The velocity after 4 seconds is -144 ft per second. 
D)  The velocity after 4 seconds is -48 ft per second. 
E)  The velocity after 4 seconds is -288 ft per second. 
A)  The velocity after 4 seconds is -80 ft per second. 
B)  The velocity after 4 seconds is -112 ft per second. 
C)  The velocity after 4 seconds is -144 ft per second. 
D)  The velocity after 4 seconds is -48 ft per second. 
E)  The velocity after 4 seconds is -288 ft per second.

Question 20

Given the derivative below find the requested higher-order derivative. ​   ,   .
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A point is moving along the graph of the function such that centimeters per second. Find when .

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

Differentiate the function .

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

Find by implicit differentiation. .

The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute. Find the rate of change of area, A, when the radius is 3.

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 1,366 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.

Find by implicit differentiation.

Differentiate the function .

Find if .

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall.

Find the derivative of the function .

Find by implicit differentiation.

Evaluate the derivative of the function at the point .

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 1,372 feet tall. Determine the velocity function for the coin.

Find by implicit differentiation.

Find the derivative of the function .

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Round your answer to 5 decimal places. ,

A ball is thrown straight down from the top of a 220-ft building with an initial velocity of -16 ft per second. The position function is . What is the velocity of the ball after 4 seconds?

Given the derivative below find the requested higher-order derivative. , .

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

A point is moving along the graph of the function such that centimeters per second. Find when . ​

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

Differentiate the function . ​

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

Find by implicit differentiation. ​ . ​

The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute. ​ Find the rate of change of area, A, when the radius is 3. ​

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 1,366 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places. ​

Find by implicit differentiation. ​ ​

Differentiate the function . ​

Find if . ​

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall. ​

Find the derivative of the function . ​

Find by implicit differentiation. ​ ​

Evaluate the derivative of the function at the point . ​

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 1,372 feet tall. Determine the velocity function for the coin. ​

Find by implicit differentiation. ​ ​

Find the derivative of the function . ​

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Round your answer to 5 decimal places. ​ , ​

A ball is thrown straight down from the top of a 220-ft building with an initial velocity of -16 ft per second. The position function is . What is the velocity of the ball after 4 seconds? ​

Given the derivative below find the requested higher-order derivative. ​ , . ​

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

A point is moving along the graph of the function such that centimeters per second. Find when .

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

Differentiate the function .

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

Find by implicit differentiation. .

The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute. Find the rate of change of area, A, when the radius is 3.

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 1,366 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.

Find by implicit differentiation.

Differentiate the function .

Find if .

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall.

Find the derivative of the function .

Find by implicit differentiation.

Evaluate the derivative of the function at the point .

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 1,372 feet tall. Determine the velocity function for the coin.

Find by implicit differentiation.

Find the derivative of the function .

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Round your answer to 5 decimal places. ,

A ball is thrown straight down from the top of a 220-ft building with an initial velocity of -16 ft per second. The position function is . What is the velocity of the ball after 4 seconds?

Given the derivative below find the requested higher-order derivative. , .