Question 1

Which of the given points are the points on the hyperboloid   where the normal line is parallel to the line that joins the points   and   .
Select all that apply.

Accepted Answer

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

Question 2

Find the directional derivative of   at the point (1, 3) in the direction toward the point (3, 1). Select the correct answer.

Accepted Answer

A)    
B)    
C) 28 
D)    
E) none of these 
A)    
B)    
C) 28 
D)    
E) none of these

Question 3

Sketch the level curves   of the function for the indicated values of k.

Accepted Answer

The answer of Sketch the level curves   of...

Question 4

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

Accepted Answer

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

Question 5

Find   for   .

Accepted Answer

The answer of Find   for   ....

Question 6

Find three positive real numbers whose sum is 388 and whose product is as large as possible.

Accepted Answer

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

Question 7

Find the equation of the normal line to the given surface at the specified point.

Accepted Answer

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

Question 8

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

Accepted Answer

Min at @#IMG-DLM& , @#IMG-DLM& , Max poi

Question 9

Find the limit.

Accepted Answer

The answer of Find the limit.  ...

Question 10

Use spherical coordinates to find the limit.

Accepted Answer

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

Question 11

The height of a hill (in feet) is given by   where x is the distance (in miles) east and y is the distance (in miles) north of your cabin. If you are at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of change of the height of the hill (a) in a northerly direction and (b) in an easterly direction?

Accepted Answer

A) (a) 570 ft/mi, (b) 690 ft/mi 
B) (a) -570 ft/mi, (b) 690 ft/mi 
C) (a) 690 ft/mi, (b) 570 ft/mi 
D) (a) 690 ft/mi, (b) -570 ft/mi 
A) (a) 570 ft/mi, (b) 690 ft/mi 
B) (a) -570 ft/mi, (b) 690 ft/mi 
C) (a) 690 ft/mi, (b) 570 ft/mi 
D) (a) 690 ft/mi, (b) -570 ft/mi

Question 12

Determine the largest set on which the function is continuous.

Accepted Answer

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

Question 13

Use the equation   to find   .

Accepted Answer

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

Question 14

Find the equation of the normal line to the given surface at the specified point.

Accepted Answer

The answer of Find the equation of the normal line...

Question 15

A contour map for a function f is shown. Use it to estimate the value of   .

Accepted Answer

A) 28 
B)    
C) 48 
D) 35 
E) 78 
A) 28 
B)    
C) 48 
D) 35 
E) 78

Question 16

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 17

Find   for   .

Accepted Answer

The answer of Find   for   ....

Question 18

Find   for   .

Accepted Answer

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

Question 19

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 20

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

The answer of The ellipsoid   intersects the plane...

Which of the given points are the points on the hyperboloid where the normal line is parallel to the line that joins the points and . Select all that apply.

Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1). Select the correct answer.

Sketch the level curves of the function for the indicated values of k.

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

Find for .

Find three positive real numbers whose sum is 388 and whose product is as large as possible.

Find the equation of the normal line to the given surface at the specified point.

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

Find the limit.

Use spherical coordinates to find the limit.

Determine the largest set on which the function is continuous.

Use the equation to find .

Find the equation of the normal line to the given surface at the specified point.

A contour map for a function f is shown. Use it to estimate the value of .

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

Find for .

Find for .

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

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

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

Which of the given points are the points on the hyperboloid where the normal line is parallel to the line that joins the points and . Select all that apply.

Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1). Select the correct answer.

Sketch the level curves of the function for the indicated values of k.

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

Find for .

Find three positive real numbers whose sum is 388 and whose product is as large as possible.

Find the equation of the normal line to the given surface at the specified point.

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

Find the limit.

Use spherical coordinates to find the limit.

Determine the largest set on which the function is continuous.

Use the equation to find .

Find the equation of the normal line to the given surface at the specified point.

A contour map for a function f is shown. Use it to estimate the value of .

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

Find for .

Find for .

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

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

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