Question 1

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

Accepted Answer

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

Question 2

Use Lagrange multipliers to find the maximum and minimum values of the function   subject to the constraints   and   .

Accepted Answer

The answer of Use Lagrange multipliers to find the maximum...

Question 3

Use the definition of partial derivatives as limits to find   if   .

Accepted Answer

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

Question 4

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 5

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 10 cm if the tin is 0.04 cm thick.

Accepted Answer

The answer of Use differentials to estimate the amount of...

Question 6

Find the indicated partial derivative.

Accepted Answer

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

Question 7

Two contour maps are shown.One is for a function f whose graph is a cone.The other is for a function g whose graph is a paraboloid.Which is the contour map of a cone?

Accepted Answer

A)  II 
B)  I 
C)  impossible to determine 
A)  II 
B)  I 
C)  impossible to determine

Question 8

Use the Chain Rule to find   .

Accepted Answer

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

Question 9

Find all the second partial derivatives.

Accepted Answer

The answer of Find all the second partial derivatives. ...

Question 10

If   use the gradient vector   to find the tangent line to the level curve   at the point   .

Accepted Answer

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

Question 11

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Accepted Answer

The answer of Use Lagrange multipliers to find the minimum...

Question 12

Find and sketch the domain of the function

Accepted Answer

The answer of Find and sketch the domain of the...

Question 13

Find three positive numbers whose sum is 400 and whose product is a maximum.

Accepted Answer

The answer of Find three positive numbers whose sum is...

Question 14

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

Accepted Answer

Relative m

Question 15

Evaluate the limit.

Accepted Answer

A)  1 
B)  0 
C)    
D)  2 
E)  the limit does not exist 
A)  1 
B)  0 
C)    
D)  2 
E)  the limit does not exist

Question 16

Describe the level surfaces of the function   .

Accepted Answer

A family o

Question 17

Use implicit differentiation to find

Accepted Answer

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

Question 18

Find the limit

Accepted Answer

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

Question 19

A cardboard box without a lid is to have a volume of   cm   .Find the dimensions that minimize the amount of cardboard used.

Accepted Answer

The answer of A cardboard box without a lid is...

Question 20

Find equations for the tangent plane and the normal line to the surface with equation   at the point

Accepted Answer

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

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

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the constraints and .

Use the definition of partial derivatives as limits to find if .

Find the differential of the function.

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 10 cm if the tin is 0.04 cm thick.

Find the indicated partial derivative.

Two contour maps are shown.One is for a function f whose graph is a cone.The other is for a function g whose graph is a paraboloid.Which is the contour map of a cone?

Use the Chain Rule to find .

Find all the second partial derivatives.

If use the gradient vector to find the tangent line to the level curve at the point .

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Find and sketch the domain of the function

Find three positive numbers whose sum is 400 and whose product is a maximum.

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

Evaluate the limit.

Describe the level surfaces of the function .

Use implicit differentiation to find

Find the limit

A cardboard box without a lid is to have a volume of cm .Find the dimensions that minimize the amount of cardboard used.

Find equations for the tangent plane and the normal line to the surface with equation at the point

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

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

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the constraints and .

Use the definition of partial derivatives as limits to find if .

Find the differential of the function.

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 10 cm if the tin is 0.04 cm thick.

Find the indicated partial derivative.

Two contour maps are shown.One is for a function f whose graph is a cone.The other is for a function g whose graph is a paraboloid.Which is the contour map of a cone?

Use the Chain Rule to find .

Find all the second partial derivatives.

If use the gradient vector to find the tangent line to the level curve at the point .

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Find and sketch the domain of the function

Find three positive numbers whose sum is 400 and whose product is a maximum.

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

Evaluate the limit.

Describe the level surfaces of the function .

Use implicit differentiation to find

Find the limit

A cardboard box without a lid is to have a volume of cm .Find the dimensions that minimize the amount of cardboard used.

Find equations for the tangent plane and the normal line to the surface with equation at the point

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