Question 1

Compute   and dy for the given values of x and   .

Accepted Answer

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E)

Question 2

Let   . Find the derivative   of  f.

Accepted Answer

The answer of Let   . Find the derivative...

Question 3

The quantity Q of charge in coulombs C that has passed through a point in a wire up to time t (measured in seconds) is given by   . Find the current when   .

Accepted Answer

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

Question 4

A television camera is positioned 4,600 ft from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and its speed is 680 ft/s when it has risen 2,600 ft. If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at this moment? Round the result to the nearest thousandth.

Accepted Answer

The answer of A television camera is positioned 4,600 ft...

Question 5

Find the derivative of the function. f (x) = 6 sin x + 2x + 9

Accepted Answer

A) 6 cos x + 2 
B) -6 sin x + 2 
C) -6 cos x + 2 
D) 6 sin x + 2 
A) 6 cos x + 2 
B) -6 sin x + 2 
C) -6 cos x + 2 
D) 6 sin x + 2

Question 6

A water trough is 20 m long and a cross-section has the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 60 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of   , how fast is the water level rising when the water is   cm deep? Round the result to the nearest hundredth.

Accepted Answer

The answer of A water trough is 20 m long...

Question 7

Find an equation of the tangent line to the curve.

Accepted Answer

The answer of Find an equation of the tangent line...

Question 8

Suppose the daily total cost (in dollars) of manufacturing x televisions is   What is the marginal cost when x = 600? What is the actual cost incurred in manufacturing the 601st television?

Accepted Answer

A) $348.00, $348.58 
B) $186.67, $186.94 
C) $348.00, $348.46 
D) $186.67, $186.98 
A) $348.00, $348.58 
B) $186.67, $186.94 
C) $348.00, $348.46 
D) $186.67, $186.98

Question 9

Find the limit if

Accepted Answer

The answer of Find the limit if   ...

Question 10

Sketch the graph of the derivative   of the function f whose graph is given.

Accepted Answer

The answer of Sketch the graph of the derivative ...

Question 11

Use the Product Rule to find the derivative of the function.

Accepted Answer

A) 4x2 + 16 
B) 4x 
C) 2x + 2 
D)    
A) 4x2 + 16 
B) 4x 
C) 2x + 2 
D)

Question 12

Differentiate the function.

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Question 13

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s how fast is the boat approaching the dock when it is   m from the dock? Round the result to the nearest hundredth if necessary.

Accepted Answer

The answer of A boat is pulled into a dock...

Question 14

Find the given derivative by finding the first few derivatives and observing the pattern that occurs.

Accepted Answer

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B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 15

If an equation of the tangent line to the curve   at the point where   is   find   and   .

Accepted Answer

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E)

Question 16

Find an equation of the tangent line to the given curve at the indicated point.

Accepted Answer

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

Question 17

If two resistors with resistances   and   are connected in parallel, as in the figure, then the total resistance   measured in ohms ($\Omega$), is given by   . If   and   are increasing at rates of   and   respectively, how fast is   changing when   and   ?
Round the result to the nearest thousandth.

Accepted Answer

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B)    
C)    
D)    
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A)    
B)    
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Question 18

Find a third-degree polynomial Q such that Q (1) =   ,   (1) = 7,   (1) = 14, and   (1) = 18.

Accepted Answer

The answer of Find a third-degree polynomial Q such that...

Question 19

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

Accepted Answer

The answer of Find an equation of the tangent line...

Question 20

If f is the focal length of a convex lens and an object is placed at a distance v from the lens, then its image will be at a distance u from the lens, where f, v, and u are related by the lens equation   . Find the rate of change of v with respect to u.

Accepted Answer

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

Compute and dy for the given values of x and .

Let . Find the derivative of f.

The quantity Q of charge in coulombs C that has passed through a point in a wire up to time t (measured in seconds) is given by . Find the current when .

Find the derivative of the function. f (x) = 6 sin x + 2x + 9

Find an equation of the tangent line to the curve.

Suppose the daily total cost (in dollars) of manufacturing x televisions is What is the marginal cost when x = 600? What is the actual cost incurred in manufacturing the 601st television?

Find the limit if

Sketch the graph of the derivative of the function f whose graph is given.

Use the Product Rule to find the derivative of the function.

Differentiate the function.

Find the given derivative by finding the first few derivatives and observing the pattern that occurs.

If an equation of the tangent line to the curve at the point where is find and .

Find an equation of the tangent line to the given curve at the indicated point.

Find a third-degree polynomial Q such that Q (1) = , (1) = 7, (1) = 14, and (1) = 18.

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

If f is the focal length of a convex lens and an object is placed at a distance v from the lens, then its image will be at a distance u from the lens, where f, v, and u are related by the lens equation . Find the rate of change of v with respect to u.

Functions and Limits

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

Filters

Exam 2: Derivatives

Compute and dy for the given values of x and .

Let . Find the derivative of f.

The quantity Q of charge in coulombs C that has passed through a point in a wire up to time t (measured in seconds) is given by . Find the current when .

Find the derivative of the function. f (x) = 6 sin x + 2x + 9

Find an equation of the tangent line to the curve.

Suppose the daily total cost (in dollars) of manufacturing x televisions is What is the marginal cost when x = 600? What is the actual cost incurred in manufacturing the 601st television?

Find the limit if

Sketch the graph of the derivative of the function f whose graph is given.

Use the Product Rule to find the derivative of the function.

Differentiate the function.

Find the given derivative by finding the first few derivatives and observing the pattern that occurs.

If an equation of the tangent line to the curve at the point where is find and .

Find an equation of the tangent line to the given curve at the indicated point.

If two resistors with resistances and are connected in parallel, as in the figure, then the total resistance measured in ohms ( Ω\OmegaΩ ), is given by . If and are increasing at rates of and respectively, how fast is changing when and ? Round the result to the nearest thousandth.

Find a third-degree polynomial Q such that Q (1) = , (1) = 7, (1) = 14, and (1) = 18.

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

If f is the focal length of a convex lens and an object is placed at a distance v from the lens, then its image will be at a distance u from the lens, where f, v, and u are related by the lens equation . Find the rate of change of v with respect to u.

Functions and Limits

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

Filters