Question 1

Evaluate the line integral over the given curve C.   ,where C is the line segment joining (-2,-1)to (4,5)

Accepted Answer

The answer of Evaluate the line integral over the given...

Question 2

Let

Accepted Answer

The answer of Let    ...

Question 3

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives,find   where a is the constant vector.

Accepted Answer

A)  3 
B)  5 
C)  7 
D)  6 
E)  8 
A)  3 
B)  5 
C)  7 
D)  6 
E)  8

Question 4

is the surface of the box enclosed by the planes   where   are positive numbers.

Accepted Answer

A)      
B)    
C)      
D)  12   
E)  12   
A)      
B)    
C)      
D)  12   
E)  12

Question 5

Determine whether F is conservative.If so,find a function f such that   .

Accepted Answer

A)    
B)    
C)    
D)  not conservative 
A)    
B)    
C)    
D)  not conservative

Question 6

Find the curl of the vector field.

Accepted Answer

The answer of Find the curl of the vector field....

Question 7

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C.   , where C is the boundary of the region bounded by the parabolas   and   .

Accepted Answer

A)    + e 
B)    
C)    + e 
D)    
A)    + e 
B)    
C)    + e 
D)

Question 8

Set up,but do not evaluate,a double integral for the area of the surface with parametric equations

Accepted Answer

The answer of Set up,but do not evaluate,a double integral...

Question 9

Let

Accepted Answer

A)  18 
B)  45 
C)  27 
D)  9 
E)  None of these 
A)  18 
B)  45 
C)  27 
D)  9 
E)  None of these

Question 10

Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and

Accepted Answer

The answer of Find the area of the surface S...

Question 11

Find the work done by the force field   on a particle that moves along the parabola

Accepted Answer

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

Question 12

Evaluate the surface integral.Round your answer to four decimal places.   S is surface

Accepted Answer

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

Question 13

A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid

Accepted Answer

The answer of A fluid with density   flows...

Question 14

Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.

Accepted Answer

The answer of Evaluate the surface integral   for...

Question 15

,where   S consists of the hemisphere   and the disk   in the   -plane.

Accepted Answer

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

Question 16

Find the gradient vector field of

Accepted Answer

The answer of Find the gradient vector field of ...

Evaluate the line integral over the given curve C. ,where C is the line segment joining (-2,-1)to (4,5)

Let

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives,find where a is the constant vector.

is the surface of the box enclosed by the planes where are positive numbers.

Determine whether F is conservative.If so,find a function f such that .

Find the curl of the vector field.

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. , where C is the boundary of the region bounded by the parabolas and .

Set up,but do not evaluate,a double integral for the area of the surface with parametric equations

Let

Find the area of the surface S where S is the part of the plane that lies above the triangular region with vertices ,and

Find the work done by the force field on a particle that moves along the parabola

Evaluate the surface integral.Round your answer to four decimal places. S is surface

A fluid with density flows with velocity Find the rate of flow upward through the paraboloid

Evaluate the surface integral for the given vector field F and the oriented surface S.In other words,find the flux of F across S.

,where S consists of the hemisphere and the disk in the -plane.

Find the gradient vector field of

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

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Parametric Equations and Polar Coordinates

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Exam 13: Vector Calculus

Evaluate the line integral over the given curve C. ,where C is the line segment joining (-2,-1)to (4,5)

Let

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives,find where a is the constant vector.

is the surface of the box enclosed by the planes where are positive numbers.

Determine whether F is conservative.If so,find a function f such that .

Find the curl of the vector field.

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. , where C is the boundary of the region bounded by the parabolas and .

Set up,but do not evaluate,a double integral for the area of the surface with parametric equations

Let

Find the area of the surface S where S is the part of the plane that lies above the triangular region with vertices ,and

Find the work done by the force field on a particle that moves along the parabola

Evaluate the surface integral.Round your answer to four decimal places. S is surface

A fluid with density flows with velocity Find the rate of flow upward through the paraboloid

Evaluate the surface integral for the given vector field F and the oriented surface S.In other words,find the flux of F across S.

,where S consists of the hemisphere and the disk in the -plane.

Find the gradient vector field of

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Filters