Question 1

Find  , if  and  .

Accepted Answer

The answer of Find  , if  and ...

Question 2

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

The ellipsoid  intersects the plane  in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

Accepted Answer

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

Find the limit

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Find  for  .

Accepted Answer

The answer of Find  for  ....

Question 7

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

Accepted Answer

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

Question 8

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 9

Find  for the function

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Describe the level survaces of the function  .

Accepted Answer

The answer of Describe the level survaces of the function...

Question 11

Evaluate the limit.

Accepted Answer

A)   
B) 0 
C)   
D)   
E)

Question 12

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

Accepted Answer

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

Question 13

Find the directional derivative of the function  at the point  in the direction of the unit vector that makes the angle  with the positive x-axis.

Accepted Answer

A) 1 
B)   
C)   
D) 11

Question 14

Describe the level surfaces of the function  .

Accepted Answer

The answer of Describe the level surfaces of the function...

Question 15

Determine the largest set on which the function is continuous.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Determine where the function  is continuous.

Accepted Answer

A)   
B)   
C)   
D)

Question 17

Use the Chain Rule to find

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Find the dimensions of the rectangular box with largest volume if the total surface area is given as   .

Accepted Answer

A)   cm,  cm, 1.75 cm 
B)   cm, 1.75 cm, 1.75 cm 
C)   cm,  cm,
 cm 
D)   cm,  cm,
 cm 
E)   cm,  cm, 3.5 cm

Question 19

Find the indicated partial derivative.

Accepted Answer

A)   
B)   
C)   
D)   
E)

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...

Exam 11: Partial Derivatives

Find , if and .

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

The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) .

Find the differential of the function

Find the limit

Find for .

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

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

Find for the function

Describe the level survaces of the function .

Evaluate the limit.

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

Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis.

Describe the level surfaces of the function .

Determine the largest set on which the function is continuous.

Determine where the function is continuous.

Use the Chain Rule to find

Find the dimensions of the rectangular box with largest volume if the total surface area is given as .

Find the indicated partial derivative.

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