Question 1

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

Accepted Answer

maximum =

Question 2

Evaluate the limit.

Accepted Answer

A)    
B)    
C)  0 
D)    
E)    
A)    
B)    
C)  0 
D)    
E)

Question 3

Find three positive numbers whose sum is 291 and whose product is a maximum.

Accepted Answer

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

Question 4

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

Accepted Answer

A)  Saddle point   
B)  Relative minimum   
C)  Relative maximum   
D)  None 
A)  Saddle point   
B)  Relative minimum   
C)  Relative maximum   
D)  None

Question 5

Describe the level surfaces of the function   .

Accepted Answer

A family o

Question 6

Find the absolute extrema of the function   on the closed triangular region with vertices   ,   and   .

Accepted Answer

A)  Absolute minimum -5,Absolute maximum 5 
B)  Absolute minimum 0,Absolute maximum 5 
C)  Absolute minimum -5,Absolute maximum 17 
D)  Absolute minimum 5,Absolute maximum 17 
A)  Absolute minimum -5,Absolute maximum 5 
B)  Absolute minimum 0,Absolute maximum 5 
C)  Absolute minimum -5,Absolute maximum 17 
D)  Absolute minimum 5,Absolute maximum 17

Question 7

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

Accepted Answer

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

Question 8

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is 84

Accepted Answer

A)  4,8,16 
B)    ,   ,   
C)    ,   ,   
D)  32,32,32 
E)  32,   ,16 
A)  4,8,16 
B)    ,   ,   
C)    ,   ,   
D)  32,32,32 
E)  32,   ,16

Question 9

Find the shortest distance from the point   to the plane   .

Accepted Answer

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

Question 10

Use implicit differentiation to find

Accepted Answer

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

Question 11

Determine the largest set on which the function is continuous.

Accepted Answer

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

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

Evaluate the limit.

Find three positive numbers whose sum is 291 and whose product is a maximum.

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

Describe the level surfaces of the function .

Find the absolute extrema of the function on the closed triangular region with vertices , and .

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

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is 84

Find the shortest distance from the point to the plane .

Use implicit differentiation to find

Determine the largest set on which the function is continuous.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Multiple Integrals

Vector Calculus

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Exam 11: Partial Derivatives

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

Evaluate the limit.

Find three positive numbers whose sum is 291 and whose product is a maximum.

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

Describe the level surfaces of the function .

Find the absolute extrema of the function on the closed triangular region with vertices , and .

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

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is 84

Find the shortest distance from the point to the plane .

Use implicit differentiation to find

Determine the largest set on which the function is continuous.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Multiple Integrals

Vector Calculus

Filters