Question 1

Find the limit.

Accepted Answer

The answer of Find the limit.  ...

Question 2

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 3

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

Question 4

Find the indicated partial derivative.

Accepted Answer

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

Question 5

Determine where the function   is continuous.

Accepted Answer

The answer of Determine where the function   is...

Question 6

Evaluate the limit.

Accepted Answer

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

Question 7

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 8

Find the first partial derivatives of the function

Accepted Answer

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

Question 9

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.)

Accepted Answer

A) 6.91   
B) 6.99   
C)      
D) 8.34   
E) 6.7   
A) 6.91   
B) 6.99   
C)      
D) 8.34   
E) 6.7

Question 10

Find the differential of the function

Accepted Answer

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

Question 11

Find   .

Accepted Answer

The answer of Find   .  ...

Question 12

Find   for the function   .

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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)    ,

Question 15

Use the Chain Rule to find   .

Accepted Answer

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

Question 16

Use partial derivatives to find the implicit derivative

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

Relative m

Question 19

Determine the largest set on which the function is continuous.

Accepted Answer

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

Question 20

Find all the second partial derivatives.

Accepted Answer

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

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.

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?

Find the indicated partial derivative.

Determine where the function is continuous.

Evaluate the limit.

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

Find the first partial derivatives of the function

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.)

Find the differential of the function

Find .

Find for the function .

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

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

Use the Chain Rule to find .

Use partial derivatives to find the implicit derivative

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

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

Determine the largest set on which the function is continuous.

Find all the second partial derivatives.

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

Vectors and the Geometry of Space

Multiple Integrals

Vector Calculus

Filters

Exam 11: Partial Derivatives

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.

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?

Find the indicated partial derivative.

Determine where the function is continuous.

Evaluate the limit.

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

Find the first partial derivatives of the function

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.)

Find the differential of the function

Find .

Find for the function .

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

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

Use the Chain Rule to find .

Use partial derivatives to find the implicit derivative

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

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

Determine the largest set on which the function is continuous.

Find all the second partial derivatives.

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

Vectors and the Geometry of Space

Multiple Integrals

Vector Calculus

Filters