Question 1

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 2

Use partial derivatives to find the implicit derivative

Accepted Answer

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

Question 3

Use the Chain Rule to find  where  .

Accepted Answer

8

Question 4

Use spherical coordinates to find the limit.

Accepted Answer

The answer of Use spherical coordinates to find the limit....

Question 5

Find the first partial derivatives of the function

Accepted Answer

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

Question 6

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a rate of 3.6 in/s.At what rate is the volume of the cone changing when the radius is 108 in.and the height is 132 in.?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

The length l,width w and height h of a box change with time.At a certain instant the dimensions are  and  ,and l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s.At that instant find the rates at which the surface area is changing.

Accepted Answer

The answer of The length l,width w and height h...

Question 9

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 10

Find  for the function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Find  ,if  and  .

Accepted Answer

The answer of Find  ,if  and  ....

Question 12

Find the absolute minimum value of the function  on the set D.D is the region bounded by the parabola  and the line

Accepted Answer

A)   0
B)   
C)   
D)   
E)   30

Question 13

Find the points on the surface  that are closest to the origin.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Determine the largest set on which the function is continuous.

Accepted Answer

The answer of Determine the largest set on which the...

Question 15

Find the critical points of the function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Suppose that over a certain region of space the electrical potential V is given by  . Find the rate of change of the potential at  in the direction of the vector  .

Accepted Answer

A)   44
B)   
C)   
D)   -2.91
E)   20

Question 17

Suppose (1,1)is a critical point of a function f with continuous second derivatives. In the case of  ,  ,  what can you say about f ?

Accepted Answer

A)   f has a local maximum at (1,1) 
B)   f has a saddle point at (1,1) 
C)   f has a local minimum at (1,1)

Question 18

Find  .

Accepted Answer

The answer of Find  . ...

Question 19

Find the local maximum,and minimum value and saddle points of the function.

Accepted Answer

The answer of Find the local maximum,and minimum value and...

Question 20

Determine where the function  is continuous.

Accepted Answer

A)   
B)   
C)   
D)

Exam 11: Partial Derivatives

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

Use partial derivatives to find the implicit derivative

Use the Chain Rule to find where .

Use spherical coordinates to find the limit.

Find the first partial derivatives of the function

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

The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a rate of 3.6 in/s.At what rate is the volume of the cone changing when the radius is 108 in.and the height is 132 in.?

The length l,width w and height h of a box change with time.At a certain instant the dimensions are and ,and l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s.At that instant find the rates at which the surface area is changing.

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 for the function .

Find ,if and .

Find the absolute minimum value of the function on the set D.D is the region bounded by the parabola and the line

Find the points on the surface that are closest to the origin.

Determine the largest set on which the function is continuous.

Find the critical points of the function.

Suppose that over a certain region of space the electrical potential V is given by . Find the rate of change of the potential at in the direction of the vector .

Suppose (1,1) is a critical point of a function f with continuous second derivatives. In the case of , , what can you say about f ?

Find .

Find the local maximum,and minimum value and saddle points of the function.

Determine where the function is continuous.