Deck 15: Vector Analysis

Question 1

Find the divergence of the vector field at the given point.

A)
B)
C)
D)
E)

Answer 1

Question 2

Find

A)
B)
C)
D)
E)

Answer 2

Question 3

Determine whether the vector field is conservative.

A)conservative
B)not conservative

Answer 3

not conservative

Question 4

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

A)
B)
C)
D)
E)

Question 5

Find

A)
B)
C)
D)

Question 6

Sketch several representative vectors in the vector field given by

A)
B)
C)
D)
E)

Question 7

Find the divergence of the vector field F given by

A)
B)
C)
D)
E)

Question 8

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

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

Question 9

Find the divergence at for the vector field

A)
B)
C)
D)
E)

Question 10

Compute for the vector field given by

A)
B)
C)
D)
E)

Question 11

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

A)
B)
C)
D)
E)

Question 12

Find

A)
B)
C)
D)
E)

Question 13

Find the conservative vector field for the potential function by finding its gradient.

A)
B)
C)
D)
E)

Question 14

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

A)
B)
C)
D)
E)

Question 15

Find the divergence of the vector field.

A)
B)
C)
D)
E)

Question 16

Sketch the vector field

A)
B)
C)
D)
E)

Question 17

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

A)
B)
C)
D)
E)

Question 18

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

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

Question 19

Find for the vector field given by

A)
B)
C)
D)
E)

Question 20

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

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

Question 21

Find the total mass of the wire with density

A)
B)
C)
D)
E)

Question 22

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

A)
B)
C)
D)
E)

Question 23

Evaluate the line integral along the given path.

A)
B)
C)
D)
E)

Question 24

Find the moments of inertia for a wire that lies along with density

A)
B)
C)
D)
E)

Question 25

Find the area of the lateral surface over the curve C in the xy-plane and under the surface where Lateral surface line from

A)
B)
C)
D)
E)

Question 26

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

A)
B)
C)
D)
E)

Question 27

A tractor engine has a steel component with a circular base modeled by the vector- valued function Its height is given by (All measurements of the
Component are given in centimeters.) Find the lateral surface area of the component.Round your
Answer to two decimal places.

A)
B)
C)
D)
E)

Question 28

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

A)
B)
C)
D)
E)

Question 29

Evaluate where C is represented by

A)
B)
C)
D)
E)

Question 30

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

A)
B)
C)
D)
E)

Question 31

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

A)
B)
C)
D)
E)

Question 32

Evaluate

A)
B)
C)
D)
E)

Question 33

Evaluate where C is represented by

A)
B)
C)
D)
E)

Question 34

Evaluate the integral along the path C, defined as from

A)
B)
C)
D)
E)

Question 35

Find the work done by a person weighing pounds walking exactly one revolution up a circular helical staircase of radius feet if the person rises feet.

A)
B)
C)
D)
E)