Question 1

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

Accepted Answer

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

Question 2

Use the Quotient Rule to differentiate the function   . ​

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Question 3

Find the second derivative of the function   . ​

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Question 4

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 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places. ​

Accepted Answer

A)  -257.185 ft/sec 
B)  -123.118 ft/sec 
C)  -111.364 ft/sec 
D)  -246.236 ft/sec 
E)  -235.236 ft/sec 
A)  -257.185 ft/sec 
B)  -123.118 ft/sec 
C)  -111.364 ft/sec 
D)  -246.236 ft/sec 
E)  -235.236 ft/sec

Question 5

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

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Question 6

Use implicit differentiation to find   . ​   ​

Accepted Answer

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Question 7

Describe the x-values at which the graph of the function   given below is differentiable. ​

Accepted Answer

A)    is differentiable at   . 
B)    is differentiable everywhere except at   . 
C)    is differentiable everywhere except at   . 
D)    is differentiable on the interval   ()(. 
E)    is differentiable on the interval   . 
A)    is differentiable at   . 
B)    is differentiable everywhere except at   . 
C)    is differentiable everywhere except at   . 
D)    is differentiable on the interval   ()(. 
E)    is differentiable on the interval   .

Question 8

Find the derivative of the function   . ​

Accepted Answer

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Question 9

Find the derivative of the function   . ​

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Question 10

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

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Question 11

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

Accepted Answer

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

Question 12

Use logarithmic differentiation to find the derivative of   . ​

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Question 13

When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle θ shown in the figure. Let h represent the satellite's distance from Earth's surface and let r represent Earth's radius. Find the rate at which h is changing with respect to θ when   (Assume   miles.) Round your answer to the nearest unit. ​   ​

Accepted Answer

A)  -13,683 mi/radian 
B)  -7,900 mi/radian 
C)  7,900 mi/radian 
D)  -4,561 mi/radian 
E)  13,683 mi/radian 
A)  -13,683 mi/radian 
B)  -7,900 mi/radian 
C)  7,900 mi/radian 
D)  -4,561 mi/radian 
E)  13,683 mi/radian

Question 14

Find the derivative of the function   . ​

Accepted Answer

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

Question 15

Find   by implicit differentiation given that   . ​

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Question 16

Find the derivative of the algebraic function   . ​

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Question 17

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​   ,   ​

Accepted Answer

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

Question 18

Find   if   . ​

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Question 19

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

Accepted Answer

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Question 20

Find   in terms of x and y. ​   ​

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

Use the Quotient Rule to differentiate the function .

Find the second derivative of the function .

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 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.

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

Use implicit differentiation to find .

Describe the x-values at which the graph of the function given below is differentiable.

Find the derivative of the function .

Find the derivative of the function .

Find the derivative of the function using the limiting process.

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

Use logarithmic differentiation to find the derivative of .

Find the derivative of the function .

Find by implicit differentiation given that .

Find the derivative of the algebraic function .

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find if .

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

Find in terms of x and y.

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 . ​

Use the Quotient Rule to differentiate the function . ​

Find the second derivative of the function . ​

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 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places. ​

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

Use implicit differentiation to find . ​ ​

Describe the x-values at which the graph of the function given below is differentiable. ​

Find the derivative of the function . ​

Find the derivative of the function . ​

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

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

Use logarithmic differentiation to find the derivative of . ​

Find the derivative of the function . ​

Find by implicit differentiation given that . ​

Find the derivative of the algebraic function . ​

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​ , ​

Find if . ​

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

Find in terms of x and y. ​ ​

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 .

Use the Quotient Rule to differentiate the function .

Find the second derivative of the function .

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 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.

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

Use implicit differentiation to find .

Describe the x-values at which the graph of the function given below is differentiable.

Find the derivative of the function .

Find the derivative of the function .

Find the derivative of the function using the limiting process.

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

Use logarithmic differentiation to find the derivative of .

Find the derivative of the function .

Find by implicit differentiation given that .

Find the derivative of the algebraic function .

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find if .

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

Find in terms of x and y.