Question 1

Evaluate   .

Accepted Answer

A)  10 
B)  7 
C)  1 
D)  Does not exist 
E)  12 
A)  10 
B)  7 
C)  1 
D)  Does not exist 
E)  12

Question 2

Find the minimum sum of 9x + 5y + 3z + 8 if x, y, and z are positive numbers such that xyz = 25.

Accepted Answer

The answer of Find the minimum sum of 9x +...

Question 3

Let f(x, y) = 2x + 2x4y3. Then,

Accepted Answer

A)  24x2y3 
B)  6x4y 
C)  24x3y2 
D)  24x2 
E)  24y2 
A)  24x2y3 
B)  6x4y 
C)  24x3y2 
D)  24x2 
E)  24y2

Question 4

Evaluate the limit   by converting to spherical coordinates   ,and observe that   if and only if   , since   .

Accepted Answer

Limit does

Question 5

Let   . Find   .

Accepted Answer

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

Question 6

Use the Lagrange multiplier method to find three positive numbers whose sum is 16 and whose product, x2yz is a maximum.

Accepted Answer

Question 7

Compute the local linear approximation to   at   .

Accepted Answer

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

Question 8

Evaluate   .

Accepted Answer

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

Question 9

Find   and   if   .

Accepted Answer

The answer of Find   and   if...

Question 10

Evaluate   .

Accepted Answer

A)  11664 
B)  7004 
C)  -3567 
D)  Does not exist 
E)  18 
A)  11664 
B)  7004 
C)  -3567 
D)  Does not exist 
E)  18

Question 11

Use the Lagrange multiplier method to find the volume of the largest rectangular box that can be inscribed in the ellipsoid 2x2 + 3y2 + 4z2 = 12.

Accepted Answer

@#IMG-DLM& , @#IMG-DLM& , and

Question 12

Let   , find   .

Accepted Answer

The answer of Let   , find  ...

Question 13

The level curve of   when   is

Accepted Answer

A)  a parabola 
B)  an ellipse 
C)  a circle 
D)  a point. 
E)  a hyperbola 
A)  a parabola 
B)  an ellipse 
C)  a circle 
D)  a point. 
E)  a hyperbola

Question 14

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 hypotenuse.

Accepted Answer

@#IMG-DLM& is the ma

Evaluate .

Find the minimum sum of 9x + 5y + 3z + 8 if x, y, and z are positive numbers such that xyz = 25.

Let f(x, y) = 2x + 2x⁴y³. Then,

Evaluate the limit by converting to spherical coordinates ,and observe that if and only if , since .

Let . Find .

Use the Lagrange multiplier method to find three positive numbers whose sum is 16 and whose product, x²yz is a maximum.

Compute the local linear approximation to at .

Evaluate .

Find and if .

Evaluate .

Use the Lagrange multiplier method to find the volume of the largest rectangular box that can be inscribed in the ellipsoid 2x² + 3y² + 4z² = 12.

Let , find .

The level curve of when is

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 hypotenuse.

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 .

Find the minimum sum of 9x + 5y + 3z + 8 if x, y, and z are positive numbers such that xyz = 25.

Let f(x, y) = 2x + 2x4y3. Then,

Evaluate the limit by converting to spherical coordinates ,and observe that if and only if , since .

Let . Find .

Use the Lagrange multiplier method to find three positive numbers whose sum is 16 and whose product, x2yz is a maximum.

Compute the local linear approximation to at .

Evaluate .

Find and if .

Evaluate .

Use the Lagrange multiplier method to find the volume of the largest rectangular box that can be inscribed in the ellipsoid 2x2 + 3y2 + 4z2 = 12.

Let , find .

The level curve of when is

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 hypotenuse.

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) = 2x + 2x⁴y³. Then,

Use the Lagrange multiplier method to find three positive numbers whose sum is 16 and whose product, x²yz is a maximum.

Use the Lagrange multiplier method to find the volume of the largest rectangular box that can be inscribed in the ellipsoid 2x² + 3y² + 4z² = 12.