Question 1

Determine whether   is conservative, and if so, find a potential function   of the vector field.

Accepted Answer

A)    is conservative with   
B)    is conservative with   
C)    is conservative with   
D)    is not conservative 
A)    is conservative with   
B)    is conservative with   
C)    is conservative with   
D)    is not conservative

Question 2

Set up a double integral that equals   where S is the portion of the plane   above the rectangle

Accepted Answer

The answer of Set up a double integral that equals...

Question 3

Use Stokes' Theorem to compute   for   and S is the portion of   above the xy-plane with   upward.

Accepted Answer

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

Question 4

Find the gradient field corresponding to

Accepted Answer

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

Question 5

Find a potential function and evaluate the integral   where C runs from   to

Accepted Answer

The answer of Find a potential function and evaluate the...

Question 6

Compute the work done by the force field   along the curve C, where C is the helix   from   to   .

Accepted Answer

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

Question 7

Find a parametric representation of the surface   from   to   .

Accepted Answer

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

Question 8

Evaluate the flux integral     S is the portion of   above the xy-plane (n upward)

Accepted Answer

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

Question 9

Use Green's Theorem to evaluate   where C is curve bounded by   and

Accepted Answer

A)    
B)  64 
C)    
D)  0 
A)    
B)  64 
C)    
D)  0

Question 10

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

Accepted Answer

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

Question 11

Evaluate   for   and C is the quarter circle from   to   .

Accepted Answer

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

Question 12

Determine whether   is conservative, and if so, find a potential function   of the vector field.

Accepted Answer

A)    is conservative with   
B)    is conservative with   
C)    is conservative with   
D)    is not conservative 
A)    is conservative with   
B)    is conservative with   
C)    is conservative with   
D)    is not conservative

Question 13

Use Green's Theorem to evaluate   where C is curve bounded by   and   oriented clockwise.

Accepted Answer

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

Question 14

Use Stokes' Theorem to compute   for   and S is the portion of a tetrahedron bounded by   and the coordinate planes with   and   upward.

Accepted Answer

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

Question 15

Use Stoke's Theorem to evaluate   where   C is the intersection of   and   oriented counterclockwise as viewed from above.

Accepted Answer

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

Question 16

Find equations for the flow lines of the vector field.

Accepted Answer

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

Question 17

Sketch several vectors in the vector field   .

Accepted Answer

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

Question 18

Use a line integral to compute the area of the region bounded by the ellipse   .

Accepted Answer

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

Question 19

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 20

Compute the work done by the force field   along the curve C, where C is the portion of   from   to   .

Accepted Answer

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

Determine whether is conservative, and if so, find a potential function of the vector field.

Set up a double integral that equals where S is the portion of the plane above the rectangle

Use Stokes' Theorem to compute for and S is the portion of above the xy-plane with upward.

Find the gradient field corresponding to

Find a potential function and evaluate the integral where C runs from to

Compute the work done by the force field along the curve C, where C is the helix from to .

Find a parametric representation of the surface from to .

Evaluate the flux integral S is the portion of above the xy-plane (n upward)

Use Green's Theorem to evaluate where C is curve bounded by and

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

Evaluate for and C is the quarter circle from to .

Determine whether is conservative, and if so, find a potential function of the vector field.

Use Green's Theorem to evaluate where C is curve bounded by and oriented clockwise.

Use Stokes' Theorem to compute for and S is the portion of a tetrahedron bounded by and the coordinate planes with and upward.

Use Stoke's Theorem to evaluate where C is the intersection of and oriented counterclockwise as viewed from above.

Find equations for the flow lines of the vector field.

Sketch several vectors in the vector field .

Use a line integral to compute the area of the region bounded by the ellipse .

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

Compute the work done by the force field along the curve C, where C is the portion of from to .

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

Determine whether is conservative, and if so, find a potential function of the vector field.

Set up a double integral that equals where S is the portion of the plane above the rectangle

Use Stokes' Theorem to compute for and S is the portion of above the xy-plane with upward.

Find the gradient field corresponding to

Find a potential function and evaluate the integral where C runs from to

Compute the work done by the force field along the curve C, where C is the helix from to .

Find a parametric representation of the surface from to .

Evaluate the flux integral S is the portion of above the xy-plane (n upward)

Use Green's Theorem to evaluate where C is curve bounded by and

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

Evaluate for and C is the quarter circle from to .

Determine whether is conservative, and if so, find a potential function of the vector field.

Use Green's Theorem to evaluate where C is curve bounded by and oriented clockwise.

Use Stokes' Theorem to compute for and S is the portion of a tetrahedron bounded by and the coordinate planes with and upward.

Use Stoke's Theorem to evaluate where C is the intersection of and oriented counterclockwise as viewed from above.

Find equations for the flow lines of the vector field.

Sketch several vectors in the vector field .

Use a line integral to compute the area of the region bounded by the ellipse .

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

Compute the work done by the force field along the curve C, where C is the portion of from to .

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.