Question 1

Set up a line integral to compute the area of the region bounded by   and

Accepted Answer

The answer of Set up a line integral to compute...

Question 2

Use Stokes' Theorem to compute   for   and C is the square   to   to   to   .

Accepted Answer

A)    
B)    
C)    
D)  0 
A)    
B)    
C)    
D)  0

Question 3

Find the curl of   .

Accepted Answer

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

Question 4

Evaluate   where   and C is the line segment from   to

Accepted Answer

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

Question 5

Determine whether the vector field is conservative and/or incompressible on R3.

Accepted Answer

A)  conservative and not incompressible 
B)  conservative and incompressible 
C)  incompressible and not conservative 
D)  neither incompressible nor conservative 
A)  conservative and not incompressible 
B)  conservative and incompressible 
C)  incompressible and not conservative 
D)  neither incompressible nor conservative

Question 6

Find equations for the flow lines of the velocity vector field   .

Accepted Answer

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

Question 7

Find the curl of   .

Accepted Answer

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

Question 8

Find the flux of   across the portion of   below

Accepted Answer

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

Question 9

Evaluate the flux integral     S is the sphere

Accepted Answer

A)  0 
B)    
C)    
D)    
A)  0 
B)    
C)    
D)

Question 10

Show that the line integral   is independent of the path.

Accepted Answer

The answer of Show that the line integral  ...

Question 11

Sketch the vector field.

Accepted Answer

The answer of Sketch the vector field.  ...

Question 12

Use the Divergence Theorem to compute   for   and Q bounded by the cube   ,   and   .

Accepted Answer

A)    
B)  0 
C)    
D)    
A)    
B)  0 
C)    
D)

Question 13

Find the divergence of   .

Accepted Answer

A)  0 
B)    
C)    
D)    
A)  0 
B)    
C)    
D)

Question 14

Sketch several vectors in the vector field   .

Accepted Answer

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

Question 15

Evaluate   , where C is the line segment from   to   .

Accepted Answer

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

Question 16

Evaluate   for   and C is the top half-circle   from   to   .

Accepted Answer

A)    
B)    
C)  0 
D)    
A)    
B)    
C)  0 
D)

Question 17

Find equations for the flow lines of the vector field.

Accepted Answer

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

Question 18

Find the gradient field corresponding to

Accepted Answer

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

Question 19

Compute   or   whichever is easier.   S is the part of the cone   that lies between   and

Accepted Answer

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

Question 20

Find the curl of   .

Accepted Answer

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

Set up a line integral to compute the area of the region bounded by and

Use Stokes' Theorem to compute for and C is the square to to to .

Find the curl of .

Evaluate where and C is the line segment from to

Determine whether the vector field is conservative and/or incompressible on R³.

Find equations for the flow lines of the velocity vector field .

Find the curl of .

Find the flux of across the portion of below

Evaluate the flux integral S is the sphere

Show that the line integral is independent of the path.

Sketch the vector field.

Use the Divergence Theorem to compute for and Q bounded by the cube , and .

Find the divergence of .

Sketch several vectors in the vector field .

Evaluate , where C is the line segment from to .

Evaluate for and C is the top half-circle from to .

Find equations for the flow lines of the vector field.

Find the gradient field corresponding to

Compute or whichever is easier. S is the part of the cone that lies between and

Find the curl of .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Second Order Differential Equations

Filters

Exam 16: Vector Calculus

Set up a line integral to compute the area of the region bounded by and

Use Stokes' Theorem to compute for and C is the square to to to .

Find the curl of .

Evaluate where and C is the line segment from to

Determine whether the vector field is conservative and/or incompressible on R3.

Find equations for the flow lines of the velocity vector field .

Find the curl of .

Find the flux of across the portion of below

Evaluate the flux integral S is the sphere

Show that the line integral is independent of the path.

Sketch the vector field.

Use the Divergence Theorem to compute for and Q bounded by the cube , and .

Find the divergence of .

Sketch several vectors in the vector field .

Evaluate , where C is the line segment from to .

Evaluate for and C is the top half-circle from to .

Find equations for the flow lines of the vector field.

Find the gradient field corresponding to

Compute or whichever is easier. S is the part of the cone that lies between and

Find the curl of .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Second Order Differential Equations

Filters

Determine whether the vector field is conservative and/or incompressible on R³.