Deck 15: Section 8: Vector Analysis

Question 1

Let and let S be the graph of . Verify Stokes's Theorem by evaluating as a line integral and as a double integral.

A)
B)
C)
D)
E)

Answer 1

Question 2

Let and let S be the plane in the first octant. Verify Stokes's Theorem by evaluating as a line integral and as a double integral.

A)
B)
C)
D) 0
E) 1

Answer 2

0

Question 3

Find the curl of the vector field

A)
B)
C)
D)
E)

Answer 3

Question 4

Use Stokes's Theorem to evaluate .Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.

A)
B)
C)
D)
E)

Question 5

Use Stokes's Theorem to evaluate where and S is the first-octant portion of over . Use a computer algebra system to verify your result.

A)
B)
C)
D)
E)

Question 6

Use Stokes's Theorem to evaluate where and S is .Use a computer algebra system to verify your result.

A)
B)
C)
D)
E)

Question 7

Find the curl of the vector field

A)
B)
C)
D)
E)

Question 8

Find the curl of the vector field .

A)
B)
C)
D)
E)

Question 9

Use Stokes's Theorem to evaluate Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.

A)
B)
C)
D)
E)

Question 10

Find the curl of the vector field

A)
B)
C)
D)
E)

Question 11

The motion of a liquid in a cylindrical container of radius 1 is described by the velocity field Find where S is the upper surface of the cylindrical container.

A)
B)
C)
D) 0
E)

Question 12

Verify Stokes's Theorem by evaluating as a line integral and as a double integral .

A)
B)
C)
D)
E)

Question 13

Let and let S be the graph of oriented counterclockwise. Use Stokes's Theorem to evaluate .

A)
B)
C)
D)
E)

Question 14

The motion of a liquid in a cylindrical container of radius 1 is described by the velocity field Find where S is the upper surface of the cylindrical container.

A)
B)
C)
D)
E)

Question 15

Use Stokes's Theorem to evaluate where and S is the first-octant portion of over Use a computer algebra system to verify your result.

A)
B)
C)
D)
E)

Question 16

Use Stokes's Theorem to evaluate Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above. C: triangle with vertices

A)
B)
C)
D)
E)

Question 17

Use Stokes's Theorem to evaluate where and S is over in the first octant. Use a computer algebra system to verify your result.

A) 0
B)
C)
D)
E)