Question 1

Evaluate   .

Accepted Answer

A)  41 
B)  23 
C)  101 
D)  Does not exist 
E)  4 
A)  41 
B)  23 
C)  101 
D)  Does not exist 
E)  4

Question 2

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 3

Let f(x, y) = x2 + xy + y2 - 2x - 3y + 6. Find f(3, -3).

Accepted Answer

Question 4

The legs of a right triangle are measured to be   and   inches with a maximum error of   inches in each measurement. Use differentials to estimate the maximum possible error in the calculated value of the area.

Accepted Answer

A)    is the maximum error in the area. 
B)    is the maximum error in the area. 
C)    is the maximum error in the area. 
D)    is the maximum error in the area. 
E)    is the maximum error in the area. 
A)    is the maximum error in the area. 
B)    is the maximum error in the area. 
C)    is the maximum error in the area. 
D)    is the maximum error in the area. 
E)    is the maximum error in the area.

Question 5

Let   ; Find   .

Accepted Answer

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

Question 6

A rectangular box, open at the top, is to contain   cubic inches. Find the dimensions of the box for which the surface area is a minimum.

Accepted Answer

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

Question 7

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 8

Use the chain rule to find   and   if w = -16 + ln (x2 + y2 + 2z), x = r + s, y = r - s, z = 2rs.

Accepted Answer

Question 9

The lengths and widths of a rectangle are measured with errors of at most   . Use differentials to estimate the maximum percentage error in the calculated area.

Accepted Answer

The answer of The lengths and widths of a rectangle...

Question 10

Let   . Compute the differential dz.

Accepted Answer

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

Question 11

Let   . Find   .

Accepted Answer

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

Question 12

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

Accepted Answer

Yes. Defin

Question 13

Let f(x, y, z) = 6x3y2 + 3x2z2 + 32. Find   .

Accepted Answer

A)  18x2y2 + 6xz2 
B)  18x2 + y2 + 6x + z2 
C)  36x2y + 12xz 
D)  0 
E)  18x2 + y2 + 6x - z2 
A)  18x2y2 + 6xz2 
B)  18x2 + y2 + 6x + z2 
C)  36x2y + 12xz 
D)  0 
E)  18x2 + y2 + 6x - z2

Question 14

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

Accepted Answer

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

Question 15

Let   . Find   .

Accepted Answer

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

Question 16

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

Accepted Answer

The answer of Determine whether the function   has...

Question 17

An open rectangular box is to contain 256 cubic inches. Use the Lagrange multiplier method to find the dimensions of the box which uses the least amount of material.

Accepted Answer

x = 8 in,

Question 18

Find parametric equations for the normal line to   at   .

Accepted Answer

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

Question 19

Find the gradient for f(x, y, z) = 7x4y3z.

Accepted Answer

@#LAT-DLM&f(x, y, z) = @#IMG-DLM& x³y<

Question 20

A particle is located at the point (5, 5) on a metal surface whose temperature at a point (x, y) is T(x, y) = 25 - 3x2 - 2y2. Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =

Accepted Answer

A)    
B)    
C)    
D)    
E)  1 
A)    
B)    
C)    
D)    
E)  1

Evaluate .

Evaluate .

Let f(x, y) = x² + xy + y² - 2x - 3y + 6. Find f(3, -3).

The legs of a right triangle are measured to be and inches with a maximum error of inches in each measurement. Use differentials to estimate the maximum possible error in the calculated value of the area.

Let ; Find .

A rectangular box, open at the top, is to contain cubic inches. Find the dimensions of the box for which the surface area is a minimum.

Evaluate .

Use the chain rule to find and if w = -16 + ln (x² + y² + 2z), x = r + s, y = r - s, z = 2rs.

The lengths and widths of a rectangle are measured with errors of at most . Use differentials to estimate the maximum percentage error in the calculated area.

Let . Compute the differential dz.

Let . Find .

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

Let f(x, y, z) = 6x³y² + 3x²z² + 32. Find .

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

Let . Find .

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

An open rectangular box is to contain 256 cubic inches. Use the Lagrange multiplier method to find the dimensions of the box which uses the least amount of material.

Find parametric equations for the normal line to at .

Find the gradient for f(x, y, z) = 7x⁴y³z.

A particle is located at the point (5, 5) on a metal surface whose temperature at a point (x, y) is T(x, y) = 25 - 3x² - 2y². Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =

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

Evaluate .

Evaluate .

Let f(x, y) = x2 + xy + y2 - 2x - 3y + 6. Find f(3, -3).

The legs of a right triangle are measured to be and inches with a maximum error of inches in each measurement. Use differentials to estimate the maximum possible error in the calculated value of the area.

Let ; Find .

A rectangular box, open at the top, is to contain cubic inches. Find the dimensions of the box for which the surface area is a minimum.

Evaluate .

Use the chain rule to find and if w = -16 + ln (x2 + y2 + 2z), x = r + s, y = r - s, z = 2rs.

The lengths and widths of a rectangle are measured with errors of at most . Use differentials to estimate the maximum percentage error in the calculated area.

Let . Compute the differential dz.

Let . Find .

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

Let f(x, y, z) = 6x3y2 + 3x2z2 + 32. Find .

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

Let . Find .

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

An open rectangular box is to contain 256 cubic inches. Use the Lagrange multiplier method to find the dimensions of the box which uses the least amount of material.

Find parametric equations for the normal line to at .

Find the gradient for f(x, y, z) = 7x4y3z.

A particle is located at the point (5, 5) on a metal surface whose temperature at a point (x, y) is T(x, y) = 25 - 3x2 - 2y2. Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =

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

Let f(x, y) = x² + xy + y² - 2x - 3y + 6. Find f(3, -3).

Use the chain rule to find and if w = -16 + ln (x² + y² + 2z), x = r + s, y = r - s, z = 2rs.

Let f(x, y, z) = 6x³y² + 3x²z² + 32. Find .

Find the gradient for f(x, y, z) = 7x⁴y³z.

A particle is located at the point (5, 5) on a metal surface whose temperature at a point (x, y) is T(x, y) = 25 - 3x² - 2y². Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =