Question 1

Find the gradient of the function   .

Accepted Answer

The answer of Find the gradient of the function ...

Question 2

Find the limit   Hint: If   and   then   if and only if

Accepted Answer

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

Question 3

Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f (x, y) as   .

Accepted Answer

A)    
B)    
C) 1 
D)    
E) the value cannot be determined 
A)    
B)    
C) 1 
D)    
E) the value cannot be determined

Question 4

Find   .

Accepted Answer

The answer of Find   .  ...

Question 5

Find the domain and range of the function   .

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D)    
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C)    
D)

Question 6

Find the limit

Accepted Answer

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D)

Question 7

Find   for the function   .

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

Question 8

Use the Chain Rule to find   .

Accepted Answer

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

Question 9

Find the domain and range of the function   .

Accepted Answer

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

Question 10

Find the limit

Accepted Answer

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

Question 11

Use implicit differentiation to find   .

Accepted Answer

The answer of Use implicit differentiation to find  ...

Question 12

Find the limit

Accepted Answer

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

Question 13

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Accepted Answer

maximum =

Question 14

Use partial derivatives to find the implicit partial derivatives   and

Accepted Answer

The answer of Use partial derivatives to find the implicit...

Question 15

Use the Chain Rule to find

Accepted Answer

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

Question 16

Find and classify the relative extrema and saddle points of the function   .

Accepted Answer

The answer of Find and classify the relative extrema and...

Question 17

Find the direction in which the maximum rate of change of f at the given point occurs.

Accepted Answer

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

Question 18

Find the first partial derivatives of the function.

Accepted Answer

The answer of Find the first partial derivatives of the...

Question 19

Find   for the function   .

Accepted Answer

The answer of Find   for the function ...

Question 20

Find the equation of the tangent plane to the given surface at the specified point.

Accepted Answer

The answer of Find the equation of the tangent plane...

Find the gradient of the function .

Find the limit Hint: If and then if and only if

Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f (x, y) as .

Find .

Find the domain and range of the function .

Find the limit

Find for the function .

Use the Chain Rule to find .

Find the domain and range of the function .

Find the limit

Use implicit differentiation to find .

Find the limit

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Use partial derivatives to find the implicit partial derivatives and

Use the Chain Rule to find

Find and classify the relative extrema and saddle points of the function .

Find the direction in which the maximum rate of change of f at the given point occurs.

Find the first partial derivatives of the function.

Find for the function .

Find the equation of the tangent plane to the given surface at the specified point.

Functions and Limits

Derivatives

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

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 14: Partial Derivatives

Find the gradient of the function .

Find the limit Hint: If and then if and only if

Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f (x, y) as .

Find .

Find the domain and range of the function .

Find the limit

Find for the function .

Use the Chain Rule to find .

Find the domain and range of the function .

Find the limit

Use implicit differentiation to find .

Find the limit

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Use partial derivatives to find the implicit partial derivatives and

Use the Chain Rule to find

Find and classify the relative extrema and saddle points of the function .

Find the direction in which the maximum rate of change of f at the given point occurs.

Find the first partial derivatives of the function.

Find for the function .

Find the equation of the tangent plane to the given surface at the specified point.

Functions and Limits

Derivatives

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

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters