Question 1

Calculate the area of the surface S.
-S is the portion of the sphere   +   +   = 16 between z = - 2   and z = 2   .

Accepted Answer

A)  32  $\pi$ 
B)  32    $\pi$ 
C)  16   $\pi$ 
D)  4   $\pi$ 
A)  32  $\pi$ 
B)  32    $\pi$ 
C)  16   $\pi$ 
D)  4   $\pi$

Question 2

Evaluate the work done between point 1 and point 2 for the conservative field F.
-F = 6xi + 6yj + 6zk;   ( 4, 4, 5) ,   ( 6, 9, 6)

Accepted Answer

A)  W = 630 
B)  W = -288 
C)  W = 0 
D)  W = 288 
A)  W = 630 
B)  W = -288 
C)  W = 0 
D)  W = 288

Question 3

Find the surface area of the surface S.
-S is the upper cap cut from the sphere   +   +   = 25 by the cylinder   .

Accepted Answer

A)  -20 $\pi$ 
B)  160 $\pi$ 
C)  10 
D)  20 $\pi$ 
A)  -20 $\pi$ 
B)  160 $\pi$ 
C)  10 
D)  20 $\pi$

Question 4

Find the divergence of the field F.
-F = -54x   i + 10yj + 6   k

Accepted Answer

A)  -108   + 10 
B)  10 
C)  -54   + 10 
D)  -108   
A)  -108   + 10 
B)  10 
C)  -54   + 10 
D)  -108

Question 5

Evaluate the line integral along the curve C.
-

Accepted Answer

A)  - 19/3 
B)  -19 
C)  29 
D)  29/3 
A)  - 19/3 
B)  -19 
C)  29 
D)  29/3

Question 6

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

Accepted Answer

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

Question 7

Calculate the area of the surface S.
-S is the portion of the plane 3x + 8y + 8z = 2 that lies within the cylinder   .

Accepted Answer

A)  25/8    $\pi$ 
B)  25/8   
C)  25/8  $\pi$ 
D)  25/4    $\pi$ 
A)  25/8    $\pi$ 
B)  25/8   
C)  25/8  $\pi$ 
D)  25/4    $\pi$

Question 8

Using Green's Theorem, calculate the area of the indicated region.
-The circle r(t) = ( 10 cos t)i + ( 10 sin t)j, 0 $\le$ t $\le$ 2 $\pi$

Accepted Answer

A)  10$\pi$ 
B)  2$\pi$ 
C)  20$\pi$ 
D)  100$\pi$ 
A)  10$\pi$ 
B)  2$\pi$ 
C)  20$\pi$ 
D)  100$\pi$

Question 9

Find the potential function f for the field F.   
-

Accepted Answer

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

Question 10

Solve the problem.
-The shape and density of a thin shell are indicated below. Find the coordinates of the center of mass. Shell: cone   +   -   = 0 between z = 3 and z = 4
Density: constant

Accepted Answer

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

Question 11

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
-F = (x - y)i + (x + y)j; C is the triangle with vertices at (0, 0), ( 3, 0), and (0, 10)

Accepted Answer

A)  30 
B)  60 
C)  300 
D)  0 
A)  30 
B)  60 
C)  300 
D)  0

Question 12

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 13

Calculate the flux of the field F across the closed plane curve C.
-F = xi + yj; the curve C is the counterclockwise path around the circle   +   = 16

Accepted Answer

A)  64$\pi$ 
B)  8$\pi$ 
C)  0 
D)  32$\pi$ 
A)  64$\pi$ 
B)  8$\pi$ 
C)  0 
D)  32$\pi$

Calculate the area of the surface S. -S is the portion of the sphere + + = 16 between z = - 2 and z = 2 .

Evaluate the work done between point 1 and point 2 for the conservative field F. -F = 6xi + 6yj + 6zk; ( 4, 4, 5) , ( 6, 9, 6)

Find the surface area of the surface S. -S is the upper cap cut from the sphere + + = 25 by the cylinder .

Find the divergence of the field F. -F = -54x i + 10yj + 6 k

Evaluate the line integral along the curve C. -

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

Calculate the area of the surface S. -S is the portion of the plane 3x + 8y + 8z = 2 that lies within the cylinder .

Using Green's Theorem, calculate the area of the indicated region. -The circle r(t) = ( 10 cos t)i + ( 10 sin t)j, 0 $\le$ t $\le$ 2 $\pi$

Find the potential function f for the field F. -

Solve the problem. -The shape and density of a thin shell are indicated below. Find the coordinates of the center of mass. Shell: cone + - = 0 between z = 3 and z = 4 Density: constant

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. -F = (x - y)i + (x + y)j; C is the triangle with vertices at (0, 0), ( 3, 0), and (0, 10)

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

Calculate the flux of the field F across the closed plane curve C. -F = xi + yj; the curve C is the counterclockwise path around the circle + = 16

Functions

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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

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Exam 17: Vector Calculus

Calculate the area of the surface S. -S is the portion of the sphere + + = 16 between z = - 2 and z = 2 .

Evaluate the work done between point 1 and point 2 for the conservative field F. -F = 6xi + 6yj + 6zk; ( 4, 4, 5) , ( 6, 9, 6)

Find the surface area of the surface S. -S is the upper cap cut from the sphere + + = 25 by the cylinder .

Find the divergence of the field F. -F = -54x i + 10yj + 6 k

Evaluate the line integral along the curve C. -

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

Calculate the area of the surface S. -S is the portion of the plane 3x + 8y + 8z = 2 that lies within the cylinder .

Using Green's Theorem, calculate the area of the indicated region. -The circle r(t) = ( 10 cos t)i + ( 10 sin t)j, 0 ≤\le≤ t ≤\le≤ 2 π\piπ

Find the potential function f for the field F. -

Solve the problem. -The shape and density of a thin shell are indicated below. Find the coordinates of the center of mass. Shell: cone + - = 0 between z = 3 and z = 4 Density: constant

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. -F = (x - y)i + (x + y)j; C is the triangle with vertices at (0, 0), ( 3, 0), and (0, 10)

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

Calculate the flux of the field F across the closed plane curve C. -F = xi + yj; the curve C is the counterclockwise path around the circle + = 16

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

Using Green's Theorem, calculate the area of the indicated region. -The circle r(t) = ( 10 cos t)i + ( 10 sin t)j, 0 $\le$ t $\le$ 2 $\pi$

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