Question 1

Determine whether   is conservative. If it is, find a potential function for it.( K is an arbitrary constant.)

Accepted Answer

A)    
B)    
C)    
D)    
E)  Not conservative 
A)    
B)    
C)    
D)    
E)  Not conservative

Question 2

Evaluate   where F(x, y, z) = 2y i + 2z j + 2y k and $\sigma$ is that portion of the cone   which lies in the first octant between x = 1 and x = 3. The surface is oriented by forward unit normals.

Accepted Answer

The answer of Evaluate   where F(x, y, z)...

Question 3

Determine whether   is conservative. If it is, find a potential function for it.( K is an arbitrary constant.)

Accepted Answer

A)    
B)    
C)    
D)    
E)  Not conservative 
A)    
B)    
C)    
D)    
E)  Not conservative

Question 4

Use Stokes' Theorem to evaluate   where F(x, y, z) = 5x j and $\sigma$ is that portion of the ellipsoid 4x2 + 4y2 + z2 = 8 for which z $\ge$ 0.

Accepted Answer

A)  5 
B)  0 
C)  12 
D)    
E)    
A)  5 
B)  0 
C)  12 
D)    
E)

Question 5

The work done by F(x, y) =6 x i + 6xy j along the curve x = y2 from (0, 0) to (1, 1) is

Accepted Answer

A)  4.5 
B)  9 
C)  6 
D)  12 
E)  0 
A)  4.5 
B)  9 
C)  6 
D)  12 
E)  0

Question 6

Determine whether the flow field F(x, y, z) = 5x3 i + 5y3 j + 5z3 k is free of all sources and sinks. If it is not, find the location of all sources and sinks.

Accepted Answer

Sources at

Question 7

Evaluate the surface integral   over the sphere x2 + y2 + z2 = 25.

Accepted Answer

A)  8 $\pi$ 
B)  800 $\pi$ 
C)     $\pi$ 
D)  400 $\pi$ 
A)  8 $\pi$ 
B)  800 $\pi$ 
C)     $\pi$ 
D)  400 $\pi$

Question 8

F(x, y, z) = xyz i + (y - 5) j + (z + 5) k. Find curlF.

Accepted Answer

A)  xz i 
B)  xz i - z j 
C)  xy j - xz k 
D)  xy j + xz k 
E)  xz i + z j 
A)  xz i 
B)  xz i - z j 
C)  xy j - xz k 
D)  xy j + xz k 
E)  xz i + z j

Question 9

Evaluate   where F(x, y, z) = 3x i + 3y j - 6z k and $\sigma$ is that portion of the sphere x2 + y2 + z2 = 9 which lies above the xy-plane and is oriented by upward unit normals.

Accepted Answer

A)  12 
B)  12 $\pi$ 
C)  9 
D)  0 
E)  6 
A)  12 
B)  12 $\pi$ 
C)  9 
D)  0 
E)  6

Determine whether is conservative. If it is, find a potential function for it.( K is an arbitrary constant.)

Determine whether is conservative. If it is, find a potential function for it.( K is an arbitrary constant.)

The work done by F(x, y) =6 x i + 6xy j along the curve x = y² from (0, 0) to (1, 1) is

Determine whether the flow field F(x, y, z) = 5x³ i + 5y³ j + 5z³ k is free of all sources and sinks. If it is not, find the location of all sources and sinks.

Evaluate the surface integral over the sphere x² + y² + z² = 25.

F(x, y, z) = xyz i + (y - 5) j + (z + 5) k. Find curlF.

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

Partial Derivatives

Multiple Integrals

Filters

Exam 15: Topics in Vector Calculus

Determine whether is conservative. If it is, find a potential function for it.( K is an arbitrary constant.)

Evaluate where F(x, y, z) = 2y i + 2z j + 2y k and σ\sigmaσ is that portion of the cone which lies in the first octant between x = 1 and x = 3. The surface is oriented by forward unit normals.

Determine whether is conservative. If it is, find a potential function for it.( K is an arbitrary constant.)

Use Stokes' Theorem to evaluate where F(x, y, z) = 5x j and σ\sigmaσ is that portion of the ellipsoid 4x2 + 4y2 + z2 = 8 for which z ≥\ge≥ 0.

The work done by F(x, y) =6 x i + 6xy j along the curve x = y2 from (0, 0) to (1, 1) is

Determine whether the flow field F(x, y, z) = 5x3 i + 5y3 j + 5z3 k is free of all sources and sinks. If it is not, find the location of all sources and sinks.

Evaluate the surface integral over the sphere x2 + y2 + z2 = 25.

F(x, y, z) = xyz i + (y - 5) j + (z + 5) k. Find curlF.

Evaluate where F(x, y, z) = 3x i + 3y j - 6z k and σ\sigmaσ is that portion of the sphere x2 + y2 + z2 = 9 which lies above the xy-plane and is oriented by upward unit normals.

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

Partial Derivatives

Multiple Integrals

Filters

The work done by F(x, y) =6 x i + 6xy j along the curve x = y² from (0, 0) to (1, 1) is

Determine whether the flow field F(x, y, z) = 5x³ i + 5y³ j + 5z³ k is free of all sources and sinks. If it is not, find the location of all sources and sinks.

Evaluate the surface integral over the sphere x² + y² + z² = 25.