Question 1

Let   .   is

Accepted Answer

A)  A relative maximum 
B)  A relative minimum 
C)  A saddle point 
D)  Cannot be determined 
E)  Both a relative maximum and a saddle point 
A)  A relative maximum 
B)  A relative minimum 
C)  A saddle point 
D)  Cannot be determined 
E)  Both a relative maximum and a saddle point

Question 2

Use the total differential to approximate the change in   as (x, y) varies from   to   .

Accepted Answer

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

Question 3

Use the Lagrange multiplier method to find three positive numbers whose sum is 12 and whose product, 2x2yz + 2 is a maximum.

Accepted Answer

The three positive n

Question 4

Let   ;   Find   .

Accepted Answer

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

Question 5

Let   Find   .

Accepted Answer

The answer of Let   Find   ....

Question 6

Let   . There is a critical point at

Accepted Answer

A)  (10, 4) 
B)  (5, 2) 
C)  (-10, -4) 
D)  (0, 0) 
E)  (1, 1) 
A)  (10, 4) 
B)  (5, 2) 
C)  (-10, -4) 
D)  (0, 0) 
E)  (1, 1)

Question 7

Evaluate   .

Accepted Answer

A)    
B)    
C)    
D)  Does not exist 
E)    
A)    
B)    
C)    
D)  Does not exist 
E)

Question 8

Find the local linear approximation to   at P = (12, 16).

Accepted Answer

The answer of Find the local linear approximation to ...

Question 9

Use Lagrange multipliers to find all the locations of the extreme values of   subject to   .

Accepted Answer

A)  (0, 0, 0) 
B)    
C)    
D)    
E)  There are none 
A)  (0, 0, 0) 
B)    
C)    
D)    
E)  There are none

Question 10

Let   Find   .

Accepted Answer

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

Question 11

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

Accepted Answer

A)  The maximum value is 0, and there is no minimum value. 
B)  The maximum value is   , and the minimum value is
  
C)  The maximum value is   , and the minimum value is
  
D)  The maximum value is   , and the minimum value is
  
E)  There is no maximum value, and the minimum value is 0. 
A)  The maximum value is 0, and there is no minimum value. 
B)  The maximum value is   , and the minimum value is
  
C)  The maximum value is   , and the minimum value is
  
D)  The maximum value is   , and the minimum value is
  
E)  There is no maximum value, and the minimum value is 0.

Question 12

(x2 + y2 + z2)5 = -23. Calculate   using implicit differentiation.

Accepted Answer

Question 13

Let   ; Find   .

Accepted Answer

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

Question 14

Determine whether the function   has a removable discontinuity at the origin.

Accepted Answer

Yes. Defin

Question 15

Let   ;   Find   .

Accepted Answer

A)

B)

C)

D)

E)

A)

B)

C)

D)

E)

Question 16

Let   . Find an equation of the level surface passing through   .

Accepted Answer

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

Question 17

Let   . Compute the differential dz.

Accepted Answer

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

Question 18

Find   and   if   .

Accepted Answer

The answer of Find   and   if...

Question 19

What is/are the domain restriction(s) for f(x, y) = ln(2x2y)?

Accepted Answer

A)  x > 0, y $\neq$ 0 
B)  x > 0, y > 0 
C)  x $\neq$ 0, y$\neq$ 0 
D)  No restrictions exist 
E)  x $\neq$ 0, y > 0 
A)  x > 0, y $\neq$ 0 
B)  x > 0, y > 0 
C)  x $\neq$ 0, y$\neq$ 0 
D)  No restrictions exist 
E)  x $\neq$ 0, y > 0

Question 20

Let   . Find   .

Accepted Answer

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

Let . is

Use the total differential to approximate the change in as (x, y) varies from to .

Use the Lagrange multiplier method to find three positive numbers whose sum is 12 and whose product, 2x²yz + 2 is a maximum.

Let ; Find .

Let Find .

Let . There is a critical point at

Evaluate .

Find the local linear approximation to at P = (12, 16).

Use Lagrange multipliers to find all the locations of the extreme values of subject to .

Let Find .

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

(x² + y² + z²)⁵ = -23. Calculate using implicit differentiation.

Let ; Find .

Determine whether the function has a removable discontinuity at the origin.

Let ; Find .

Let . Find an equation of the level surface passing through .

Let . Compute the differential dz.

Find and if .

What is/are the domain restriction(s) for f(x, y) = ln(2x²y)?

Let . Find .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 13: Partial Derivatives

Let . is

Use the total differential to approximate the change in as (x, y) varies from to .

Use the Lagrange multiplier method to find three positive numbers whose sum is 12 and whose product, 2x2yz + 2 is a maximum.

Let ; Find .

Let Find .

Let . There is a critical point at

Evaluate .

Find the local linear approximation to at P = (12, 16).

Use Lagrange multipliers to find all the locations of the extreme values of subject to .

Let Find .

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

(x2 + y2 + z2)5 = -23. Calculate using implicit differentiation.

Let ; Find .

Determine whether the function has a removable discontinuity at the origin.

Let ; Find .

Let . Find an equation of the level surface passing through .

Let . Compute the differential dz.

Find and if .

What is/are the domain restriction(s) for f(x, y) = ln(2x2y)?

Let . Find .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Multiple Integrals

Topics in Vector Calculus

Filters

Use the Lagrange multiplier method to find three positive numbers whose sum is 12 and whose product, 2x²yz + 2 is a maximum.

(x² + y² + z²)⁵ = -23. Calculate using implicit differentiation.

What is/are the domain restriction(s) for f(x, y) = ln(2x²y)?