Deck 17: Integrals and Vector Fields

Question 1

Find the limit.

A) Figure 5
B) Figure 8
C) Figure 1
D) Figure 3

Answer 1

B

Question 2

Evaluate the line integral along the curve C.

Answer 2

C

Question 3

Find the limit.

A) Figure 8
B) Figure 3
C) Figure 1
D) Figure 5

Answer 3

B

Question 4

Evaluate the line integral along the curve C.

Question 5

Evaluate the line integral along the curve C.

Question 6

Evaluate the line integral of f(x,y) along the curve C.

Question 7

Evaluate the line integral along the curve C.

Question 8

Evaluate the line integral along the curve C.

Question 9

Find the limit.

A) Figure 7
B) Figure 4
C) Figure 1
D) Figure 2

Question 10

Find the limit.

A) Figure 2
B) Figure 8
C) Figure 4
D) Figure 7

Question 11

Evaluate the line integral along the curve C.

Question 12

Evaluate the line integral along the curve C.

Question 13

Evaluate the line integral along the curve C.

Question 14

Find the limit.

A) Figure 8
B) Figure 1
C) Figure 3
D) Figure 5

Question 15

Find the limit.

A) Figure 2
B) Figure 6
C) Figure 4
D) Figure 7

Question 16

Evaluate the line integral of f(x,y) along the curve C.

Question 17

Evaluate the line integral along the curve C.

Question 18

Find the limit.

A) Figure 3
B) Figure 6
C) Figure 5
D) Figure 1

Question 19

Find the limit.

A) Figure 5
B) Figure 3
C) Figure 8
D) Figure 6

Question 20

Evaluate the line integral along the curve C.

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Evaluate the line integral of f(x,y) along the curve C.

Question 28

Evaluate the line integral of f(x,y) along the curve C.

Question 29

Question 30

Evaluate the line integral of f(x,y) along the curve C.

A) 200
B) 400
C) 0
D) 100

Question 31

Question 32

Question 33

Evaluate the line integral of f(x,y) along the curve C.

Question 34

Question 35

Question 36

Find the gradient field of the function.

Question 37

Question 38

Evaluate the line integral of f(x,y) along the curve C.

Question 39

Find the gradient field of the function.

Question 40

Find the gradient field of the function.

Question 41

Find the work done by F over the curve in the direction of increasing t.

Question 42

Find the work done by F over the curve in the direction of increasing t.

Question 43

Find the work done by F over the curve in the direction of increasing t.

Question 44

Calculate the circulation of the field F around the closed curve C.

Question 45

Find the work done by F over the curve in the direction of increasing t.

Question 46

Find the gradient field of the function.

Question 47

Find the gradient field of the function.

Question 48

Find the work done by F over the curve in the direction of increasing t.

Question 49

Find the gradient field of the function.

Question 50

Find the gradient field of the function.

Question 51

Find the work done by F over the curve in the direction of increasing t.

Question 52

Find the work done by F over the curve in the direction of increasing t.

Question 53

Find the work done by F over the curve in the direction of increasing t.

Question 54

Find the work done by F over the curve in the direction of increasing t.

Question 55

Find the gradient field of the function.

Question 56

Find the work done by F over the curve in the direction of increasing t.

Question 57

Calculate the circulation of the field F around the closed curve C.

Question 58

Find the gradient field of the function.
f(x, y, z) = z sin (x + y + z)

Question 59

Calculate the circulation of the field F around the closed curve C.

Question 60

Find the gradient field of the function.

Question 61

Calculate the flow in the field F along the path C.

Question 62

Calculate the flow in the field F along the path C.

A) 5
B) -4
C) - 7
D) 28

Question 63

Calculate the flow in the field F along the path C.

Question 64

Calculate the flux of the field F across the closed plane curve C.

A) 0
B) -288
C) 144
D) -144

Question 65

Calculate the flow in the field F along the path C.

Question 66

Calculate the circulation of the field F around the closed curve C.

A) 72
B) 36
C) 0
D) 6

Question 67

Calculate the flux of the field F across the closed plane curve C.
F = xi + yj; the curve C is the closed counterclockwise path around the rectangle with vertices at (0, 0), (4, 0), (4, 3), and (0, 3)

A) 24
B) 7
C) 0
D) 25

Question 68

Calculate the flux of the field F across the closed plane curve C.

A) 12
B) 2
C) 4
D) 0

Question 69

Calculate the flow in the field F along the path C.

A) 23
B) -13
C) 14
D) -8

Question 70

Calculate the flux of the field F across the closed plane curve C.

Question 71

Calculate the circulation of the field F around the closed curve C.

A) 0
B) - 11
C) 43
D) 11

Question 72

Calculate the flux of the field F across the closed plane curve C.
F = (x+y)i + xyj; the curve C is the closed counterclockwise path around the rectangle with vertices at (0, 0), (3, 0), (3, 10), and (0, 10)

A) 175
B) 85
C) 120
D) 75

Question 73

Calculate the flux of the field F across the closed plane curve C.

Question 74

Question 75

Question 76

Calculate the flux of the field F across the closed plane curve C.

Question 77

Calculate the flow in the field F along the path C.

Question 78

Calculate the flux of the field F across the closed plane curve C.

Question 79

Question 80

Calculate the circulation of the field F around the closed curve C.
F = (-x - y)i + (x + y)j , curve C is the counterclockwise path around the circle with radius 3 centered at (3, 6)