Question 1

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Accepted Answer

A) conservative with potential function   
B) conservative with potential function   
C) conservative with potential function   
D) conservative with potential function   
E) not conservative 
A) conservative with potential function   
B) conservative with potential function   
C) conservative with potential function   
D) conservative with potential function   
E) not conservative A

Question 2

Find

Accepted Answer

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

Question 3

Find the total mass of the wire with density

Accepted Answer

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

Question 4

Evaluate

Accepted Answer

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

Question 5

Determine whether the vector field is conservative.

Accepted Answer

A) conservative 
B) not conservative 
A) conservative 
B) not conservative

Question 6

Evaluate   along the path C, defined as counterclockwise along the circle

Accepted Answer

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

Question 7

Find the curl for the vector field at the given point.

Accepted Answer

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

Question 8

Find a piecewise smooth parametrization of the path C given in the following graph.

Accepted Answer

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

Question 9

Find the divergence of the vector field F given by

Accepted Answer

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

Question 10

Evaluate   along the path C, defined as y-axis from

Accepted Answer

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

Question 11

Sketch the vector field

Accepted Answer

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

Question 12

Find

Accepted Answer

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

Question 13

Evaluate the integral   along the path C, defined as y-axis from

Accepted Answer

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

Question 14

Find   for the vector field given by

Accepted Answer

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

Question 15

Find the work done by the force field   on a particle moving along the given path.   from

Accepted Answer

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

Question 16

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Accepted Answer

A) conservative with potential function   
B) conservative with potential function   
C) conservative with potential function   
D) conservative with potential function   
E) not conservative 
A) conservative with potential function   
B) conservative with potential function   
C) conservative with potential function   
D) conservative with potential function   
E) not conservative

Question 17

Evaluate the integral   along the path C, defined as   from

Accepted Answer

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

Question 18

Find the divergence of the vector field.

Accepted Answer

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

Question 19

Evaluate   where C is represented by

Accepted Answer

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

Question 20

Find the gradient vector for the scalar function.(That is, find the conservative vector field for the potential function.)

Accepted Answer

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

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Find

Find the total mass of the wire with density

Evaluate

Determine whether the vector field is conservative.

Evaluate along the path C, defined as counterclockwise along the circle

Find the curl for the vector field at the given point.

Find a piecewise smooth parametrization of the path C given in the following graph.

Find the divergence of the vector field F given by

Evaluate along the path C, defined as y-axis from

Sketch the vector field

Find

Evaluate the integral along the path C, defined as y-axis from

Find for the vector field given by

Find the work done by the force field on a particle moving along the given path. from

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Evaluate the integral along the path C, defined as from

Find the divergence of the vector field.

Evaluate where C is represented by

Find the gradient vector for the scalar function.(That is, find the conservative vector field for the potential function.)

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Additional Topics in Differential Equations

Preparation for Calculus

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Exam 15: Vector Analysis

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Find

Find the total mass of the wire with density

Evaluate

Determine whether the vector field is conservative.

Evaluate along the path C, defined as counterclockwise along the circle

Find the curl for the vector field at the given point.

Find a piecewise smooth parametrization of the path C given in the following graph.

Find the divergence of the vector field F given by

Evaluate along the path C, defined as y-axis from

Sketch the vector field

Find

Evaluate the integral along the path C, defined as y-axis from

Find for the vector field given by

Find the work done by the force field on a particle moving along the given path. from

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Evaluate the integral along the path C, defined as from

Find the divergence of the vector field.

Evaluate where C is represented by

Find the gradient vector for the scalar function.(That is, find the conservative vector field for the potential function.)

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Additional Topics in Differential Equations

Preparation for Calculus

Filters