Question 1

Select the correct Answer: for each question.
-Find an equation of the tangent line to the curve   at the point (4,1).

Accepted Answer

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D)    
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Question 2

Find the instantaneous rate of change of the function   when   Select the correct Answer

Accepted Answer

A) 64 
B)    
C) 8 
D)    
A) 64 
B)    
C) 8 
D)

Question 3

Differentiate the function.

Accepted Answer

The answer of Differentiate the function.  ...

Question 4

Find the second derivative of the function.Select the correct Answer

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Question 5

In an adiabatic process (one in which no heat transfer takes place), the pressure   and volume V   of an ideal gas such as oxygen satisfy the equation   where   is a constant.Suppose that at a certain instant of time, the volume of the gas is 2L, the pressure is 100 kPa, and the pressure is decreasing at the rate of 5 kPa/sec.Find the rate at which the volume is changing.

Accepted Answer

The answer of In an adiabatic process (one in which...

Question 6

Select the correct Answer: for each question.
-Find   in terms of

Accepted Answer

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Question 7

Select the correct Answer for each question.
-Find the derivative of the function.

Accepted Answer

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Question 8

At what point of the curve   does the tangent line have slope   Select the correct Answer

Accepted Answer

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Question 9

The quantity   of charge in coulombs   that has passed through a point in a wire up to time   (measured in seconds) is given by   Find the current when   Select the correct Answer

Accepted Answer

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Question 10

Select the correct Answer for each question.
-An equation relating the variables   and   the values of x and y, and the value of   at a particular instant of time are given.Find the value of

Accepted Answer

A) 2 
B) -2 
C) 4 
D) -4 
A) 2 
B) -2 
C) 4 
D) -4

Question 11

Find the derivative of the function.Select the correct Answer

Accepted Answer

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Question 12

Use implicit differentiation to find an equation of the tangent line to the curve at the indicated point.Select the correct Answer

Accepted Answer

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D)

Question 13

Select the correct Answer for each question.
-Find

Accepted Answer

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Question 14

Accepted Answer

The answer of  ...

Question 15

Select the correct Answer: for each question.
-Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

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C)    
D)    
E)    
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E)

Question 16

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 17

Find the rate of change of   with respect to x at the given values of   and

Accepted Answer

The answer of Find the rate of change of ...

Question 18

Select the correct Answer: for each question.
-Find the derivative of the function.

Accepted Answer

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B)    
C)    
D)    
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C)    
D)

Question 19

Evaluate

Accepted Answer

The answer of Evaluate  ...

Question 20

Use differentials to estimate the amount of paint needed to apply a coat of paint   cm thick to a hemispherical dome with diameter   m.Select the correct Answer

Accepted Answer

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Select the correct Answer: for each question. -Find an equation of the tangent line to the curve at the point (4,1).

Find the instantaneous rate of change of the function when Select the correct Answer

Differentiate the function.

Find the second derivative of the function.Select the correct Answer

Select the correct Answer: for each question. -Find in terms of

Select the correct Answer for each question. -Find the derivative of the function.

At what point of the curve does the tangent line have slope Select the correct Answer

The quantity of charge in coulombs that has passed through a point in a wire up to time (measured in seconds) is given by Find the current when Select the correct Answer

Select the correct Answer for each question. -An equation relating the variables and the values of x and y, and the value of at a particular instant of time are given.Find the value of

Find the derivative of the function.Select the correct Answer

Use implicit differentiation to find an equation of the tangent line to the curve at the indicated point.Select the correct Answer

Select the correct Answer for each question. -Find

Select the correct Answer: for each question. -Use logarithmic differentiation to find the derivative of the function.

Find the derivative of the function.

Find the rate of change of with respect to x at the given values of and

Select the correct Answer: for each question. -Find the derivative of the function.

Evaluate

Use differentials to estimate the amount of paint needed to apply a coat of paint cm thick to a hemispherical dome with diameter m.Select the correct Answer

Functions and Models

Limits and Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 3: Differentiation Rules

Select the correct Answer: for each question. -Find an equation of the tangent line to the curve at the point (4,1).

Find the instantaneous rate of change of the function when Select the correct Answer

Differentiate the function.

Find the second derivative of the function.Select the correct Answer

Select the correct Answer: for each question. -Find in terms of

Select the correct Answer for each question. -Find the derivative of the function.

At what point of the curve does the tangent line have slope Select the correct Answer

The quantity of charge in coulombs that has passed through a point in a wire up to time (measured in seconds) is given by Find the current when Select the correct Answer

Select the correct Answer for each question. -An equation relating the variables and the values of x and y, and the value of at a particular instant of time are given.Find the value of

Find the derivative of the function.Select the correct Answer

Use implicit differentiation to find an equation of the tangent line to the curve at the indicated point.Select the correct Answer

Select the correct Answer for each question. -Find

Select the correct Answer: for each question. -Use logarithmic differentiation to find the derivative of the function.

Find the derivative of the function.

Find the rate of change of with respect to x at the given values of and

Select the correct Answer: for each question. -Find the derivative of the function.

Evaluate

Use differentials to estimate the amount of paint needed to apply a coat of paint cm thick to a hemispherical dome with diameter m.Select the correct Answer

Functions and Models

Limits and Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters