Deck 15: Section 6: Vector Analysis

Question 1

Evaluate , where .

A)
B)
C)
D)
E)

Answer 1

Question 2

Evaluate , where .

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the flux of over the closed surface (let be the outward unit normal vector of the surface). S: cube bounded by

A) 200
B) 800
C) 400
D) 1,000
E) 600

Answer 3

400

Question 4

Find the flux of through S, , where is the upward unit normal vector to S. , first octant

A)
B)
C)
D)
E)

Question 5

Let S be the surface oriented upwards. Use a computer algebra system to find the rate of mass flow of a fluid of density through S if the velocity field is given by .

A)
B)
C)
D)
E)

Question 6

Find the mass of the surface lamina S of density .

A)
B)
C)
D)
E)

Question 7

Evaluate , where S is , first octant.

A)
B)
C)
D)
E)

Question 8

Use a computer algebra system to evaluate where S is . Round your answer to two decimal places.

A) 124.82
B) 1.07
C) 62.41
D) 141.01
E) 64.00

Question 9

Evaluate , where and S is given by .

A) 10,000
B)
C)
D)
E)

Question 10

Find the flux of through S, , where is the upward unit normal vector to S.

A)
B)
C)
D)
E)

Question 11

Evaluate , where and S is given by .

A)
B)
C)
D)
E)

Question 12

Find for the lamina with uniform density of 1. Use a computer algebra system to verify your result.

A)
B)
C)
D)
E)

Question 13

Evaluate , where .

A)
B)
C)
D)
E)

Question 14

Use a computer algebra system to evaluate where S is . Round your answer to two decimal places.

A) -475.02
B) -496.00
C) -203.00
D) -971.38
E)

Question 15

Find the flux of through where N is the upward unit normal vector to S.

A) 2
B) 3
C) 10
D)
E) 5

Question 16

Let be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere and its circular base in the xy-plane.

A)
B)
C)
D)
E)

Question 17

Evaluate , where and S is given by .

A) 8
B) 32
C) 16
D) 96
E) 512

Question 18

Evaluate , where .

A)
B)
C)
D)
E)