Question 1

Find the potential function f for the field F.   
-F = (y - z)i + (x + 2y - z)j - (x + y)k

Accepted Answer

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

Question 2

Using Green's Theorem, calculate the area of the indicated region.
-The area bounded above by y = 5x and below by y = 7

Accepted Answer

A)  125/147 
B)  25/294 
C)  625/588 
D)  125/294 
A)  125/147 
B)  25/294 
C)  625/588 
D)  125/294

Question 3

Find the flux of the vector field F across the surface S in the indicated direction.
-F =   yi - zk; S is portion of the cone z = 2   between z = 0 and z = 4; direction is outward

Accepted Answer

A)  - 32$\pi$ 
B)  - 32/3 $\pi$ 
C)  - 16/3 
D)  32/3 $\pi$ 
A)  - 32$\pi$ 
B)  - 32/3 $\pi$ 
C)  - 16/3 
D)  32/3 $\pi$

Question 4

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
-F = ( 6x + 6y)i + ( 9x - 2y)j; C is the region bounded above by y = -5   + 112 and below by   in the first quadrant

Accepted Answer

A)  -1332 
B)  - 2180 
C)  896 
D)  -   
A)  -1332 
B)  - 2180 
C)  896 
D)  -

Question 5

Using Green's Theorem, calculate the area of the indicated region.
-The area bounded above by y = 10 and below by y =

Accepted Answer

A)  160/3 
B)  0 
C)  640/3 
D)  320/3 
A)  160/3 
B)  0 
C)  640/3 
D)  320/3

Question 6

Find the divergence of the field F.
-F = -7   i + 4xyj + 5xzk

Accepted Answer

A)  -56   + 4y + 5z 
B)  -56   + 9x 
C)  -47 
D)  -56   + 9x - 47 
A)  -56   + 4y + 5z 
B)  -56   + 9x 
C)  -47 
D)  -56   + 9x - 47

Question 7

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
-F = ln (   +   )i +     j; C is the region defined by the polar coordinate inequalities 1 $\le$ r $\le$ 7 and

Accepted Answer

A)  96 
B)  -12 
C)  50 
D)  0 
A)  96 
B)  -12 
C)  50 
D)  0

Question 8

Find the surface area of the surface S.
-S is the cap cut from the sphere   +   +   = 9 by the cone z = 8   .

Accepted Answer

A)  9    $\pi$ 
B)  18    $\pi$ 
C)  9    $\pi$ 
D)  9   
A)  9    $\pi$ 
B)  18    $\pi$ 
C)  9    $\pi$ 
D)  9

Question 9

Evaluate the line integral of f(x,y) along the curve C.
-f(x, y) = cos x + sin y, C: y = x, 0$\le$x $\le$

Accepted Answer

A)    
B)  2 
C)  0 
D)  2   
A)    
B)  2 
C)  0 
D)  2

Question 10

Sketch the vector field in the plane along with its horizontal and vertical components at a representative assortment of points on the circle  xS1U1P12S1S1P0 + yS1U1P12S1S1P0  = 4. 
-F =   i -   j

Accepted Answer

The answer of Sketch the vector field in the plane...

Question 11

Find the flux of the curl of field F through the shell S.
-F = -7zi + 6xj + 5yk; S is the portion of the cone z = 3   below the plane z = 1

Accepted Answer

A)  - 1/3 $\pi$ 
B)  - 4/3  $\pi$ 
C)  - 2/3  $\pi$ 
D)  4/3  $\pi$ 
A)  - 1/3 $\pi$ 
B)  - 4/3  $\pi$ 
C)  - 2/3  $\pi$ 
D)  4/3  $\pi$

Question 12

Find the gradient field F of the function f.        
-f(x, y, z) =

Accepted Answer

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

Question 13

Calculate the flux of the field F across the closed plane curve C.
-  the curve C is the closed counterclockwise path around the triangle with vertices at

Accepted Answer

A)  70 
B)  70/3 
C)  -10 
D)  0 
A)  70 
B)  70/3 
C)  -10 
D)  0

Question 14

Find the flux of the vector field F across the surface S in the indicated direction.
-F(x, y, z) = xzi + yzj + k , S is the cap cut from the sphere   +   +   = 16 by the plane   direction is outward

Accepted Answer

A)  60 $\pi$ 
B)  - 84 $\pi$ 
C)  84 $\pi$ 
D)  168$\pi$ 
A)  60 $\pi$ 
B)  - 84 $\pi$ 
C)  84 $\pi$ 
D)  168$\pi$

Question 15

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

Accepted Answer

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

Question 16

Evaluate the line integral along the curve C.
-  ds , C is the straight-line segment x = 0, y = 3 - t, z = t from (0, 3, 0) to

Accepted Answer

A)  9 
B)  9/2 
C)  0 
D)  9   
A)  9 
B)  9/2 
C)  0 
D)  9

Question 17

Find the mass of the wire that lies along the curve r and has density δ.
-

Accepted Answer

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

Question 18

Find the surface area of the surface S.
-S is the paraboloid   +   - z = 0 between the planes z =   and z = 6.

Accepted Answer

A)  61 / 4  $\pi$ 
B)  61 /3  $\pi$ 
C)  61/ 6  $\pi$ 
D)  61 / 12  $\pi$ 
A)  61 / 4  $\pi$ 
B)  61 /3  $\pi$ 
C)  61/ 6  $\pi$ 
D)  61 / 12  $\pi$

Question 19

Evaluate the surface integral of G over the surface S.
-S is the hemisphere   +   +   = 11, z$\neq$ 0; G(x,y,z) =

Accepted Answer

A)  242/3  $\pi$ 
B)  121 /3  $\pi$ 
C)  484  $\pi$ 
D)  44/3  $\pi$ 
A)  242/3  $\pi$ 
B)  121 /3  $\pi$ 
C)  484  $\pi$ 
D)  44/3  $\pi$

Question 20

Find the work done by F over the curve in the direction of increasing t.
-F = 5yi +   j + ( 5x + 2z)k; C: r(t) = ti +   j + tk, 0 $\le$ t $\le$ 2

Accepted Answer

A)  W = 47 + 20   
B)  W =   +   
C)  W =   + 20   
D)  W = 0 
A)  W = 47 + 20   
B)  W =   +   
C)  W =   + 20   
D)  W = 0

Find the potential function f for the field F. -F = (y - z)i + (x + 2y - z)j - (x + y)k

Using Green's Theorem, calculate the area of the indicated region. -The area bounded above by y = 5x and below by y = 7

Find the flux of the vector field F across the surface S in the indicated direction. -F = yi - zk; S is portion of the cone z = 2 between z = 0 and z = 4; direction is outward

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. -F = ( 6x + 6y)i + ( 9x - 2y)j; C is the region bounded above by y = -5 + 112 and below by in the first quadrant

Using Green's Theorem, calculate the area of the indicated region. -The area bounded above by y = 10 and below by y =

Find the divergence of the field F. -F = -7 i + 4xyj + 5xzk

Find the surface area of the surface S. -S is the cap cut from the sphere + + = 9 by the cone z = 8 .

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = cos x + sin y, C: y = x, 0 $\le$ x $\le$ $Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = cos x + sin y, C: y = x, 0 \le x \le$

Sketch the vector field in the plane along with its horizontal and vertical components at a representative assortment of points on the circle x² + y² = 4. -F = i - j

Find the flux of the curl of field F through the shell S. -F = -7zi + 6xj + 5yk; S is the portion of the cone z = 3 below the plane z = 1

Find the gradient field F of the function f. -f(x, y, z) =

Calculate the flux of the field F across the closed plane curve C. - the curve C is the closed counterclockwise path around the triangle with vertices at

Find the flux of the vector field F across the surface S in the indicated direction. -F(x, y, z) = xzi + yzj + k , S is the cap cut from the sphere + + = 16 by the plane direction is outward

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

Evaluate the line integral along the curve C. - ds , C is the straight-line segment x = 0, y = 3 - t, z = t from (0, 3, 0) to

Find the mass of the wire that lies along the curve r and has density δ. -

Find the surface area of the surface S. -S is the paraboloid + - z = 0 between the planes z = and z = 6.

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Exam 17: Vector Calculus

Find the potential function f for the field F. -F = (y - z)i + (x + 2y - z)j - (x + y)k

Using Green's Theorem, calculate the area of the indicated region. -The area bounded above by y = 5x and below by y = 7

Find the flux of the vector field F across the surface S in the indicated direction. -F = yi - zk; S is portion of the cone z = 2 between z = 0 and z = 4; direction is outward

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. -F = ( 6x + 6y)i + ( 9x - 2y)j; C is the region bounded above by y = -5 + 112 and below by in the first quadrant

Using Green's Theorem, calculate the area of the indicated region. -The area bounded above by y = 10 and below by y =

Find the divergence of the field F. -F = -7 i + 4xyj + 5xzk

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. -F = ln ( + )i + j; C is the region defined by the polar coordinate inequalities 1 ≤\le≤ r ≤\le≤ 7 and

Find the surface area of the surface S. -S is the cap cut from the sphere + + = 9 by the cone z = 8 .

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = cos x + sin y, C: y = x, 0 ≤\le≤ x ≤\le≤

Sketch the vector field in the plane along with its horizontal and vertical components at a representative assortment of points on the circle x2 + y2 = 4. -F = i - j

Find the flux of the curl of field F through the shell S. -F = -7zi + 6xj + 5yk; S is the portion of the cone z = 3 below the plane z = 1

Find the gradient field F of the function f. -f(x, y, z) =

Calculate the flux of the field F across the closed plane curve C. - the curve C is the closed counterclockwise path around the triangle with vertices at

Find the flux of the vector field F across the surface S in the indicated direction. -F(x, y, z) = xzi + yzj + k , S is the cap cut from the sphere + + = 16 by the plane direction is outward

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

Evaluate the line integral along the curve C. - ds , C is the straight-line segment x = 0, y = 3 - t, z = t from (0, 3, 0) to

Find the mass of the wire that lies along the curve r and has density δ. -

Find the surface area of the surface S. -S is the paraboloid + - z = 0 between the planes z = and z = 6.

Evaluate the surface integral of G over the surface S. -S is the hemisphere + + = 11, z ≠\neq= 0; G(x,y,z) =

Find the work done by F over the curve in the direction of increasing t. -F = 5yi + j + ( 5x + 2z)k; C: r(t) = ti + j + tk, 0 ≤\le≤ t ≤\le≤ 2

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Filters

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = cos x + sin y, C: y = x, 0 $\le$ x $\le$ $Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = cos x + sin y, C: y = x, 0 \le x \le$

Sketch the vector field in the plane along with its horizontal and vertical components at a representative assortment of points on the circle x² + y² = 4. -F = i - j