Question 1

Show that F is conservative and find a function f such that   and use this result to evaluate   where C is any path from

Accepted Answer

The answer of Show that F is conservative and find...

Question 2

Select the correct Answer for each question.
-Use Green's Theorem to evaluate the line integral along the positively oriented closed curve     where C is the triangle with vertices

Accepted Answer

A) 6 
B) 60 
C) 30 
D) 66 
A) 6 
B) 60 
C) 30 
D) 66 C

Question 3

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

Accepted Answer

The answer of Evaluate the surface integral.Round yourAnswer to four...

Question 4

Use a computer algebra system to compute the flux of F across S.S is the surface of the cube cut from the first octant by the planes   Select the correct Answer

Accepted Answer

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

Question 5

Find the work done by the force field F on a particle that moves along the curve C.Select the correct Answer

Accepted Answer

A) 17 
B) 19 
C) 34 
D)    
A) 17 
B) 19 
C) 34 
D)

Question 6

Use the Divergence Theorem to calculate the surface integral   that is, calculate the flux of across .   S is the surface of the box bounded by the coordinate planes and the planes   Select the correct Answer

Accepted Answer

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

Question 7

Use Stoke's theorem to evaluate   C is the curve of intersection of the hyperbolic paraboloid   and the cylinder   oriented counterclockwise as viewed from above.

Accepted Answer

The answer of Use Stoke's theorem to evaluate  ...

Question 8

Find a parametric representation for the part of the plane   that lies inside the cylinder

Accepted Answer

The answer of Find a parametric representation for the part...

Question 9

Use Stoke's theorem to evaluate   and C is the boundary of the part of the plane   in the first octant.Select the correct Answer

Accepted Answer

A) 69 
B) 16 
C) 49 
D) 0 
E) 23 
A) 69 
B) 16 
C) 49 
D) 0 
E) 23

Question 10

Select the correct Answer for each question.
-Evaluate     S is the part of the torus with vector representation

Accepted Answer

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

Question 11

Use Stoke's theorem to evaluate     C is the curve of intersection of the plane   and the cylinder

Accepted Answer

The answer of Use Stoke's theorem to evaluate  ...

Question 12

Find the area of the surface.The part of the paraboloid ; ,

Accepted Answer

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

Question 13

Determine whether or not F is a conservative vector field.If it is, find a function   such that

Accepted Answer

The answer of   Determine whether or not F...

Question 14

Use Stoke's theorem to evaluate   C is the curve of intersection of the hyperbolic paraboloid   and the cylinder   oriented counterclockwise as viewed from above.

Accepted Answer

The answer of Use Stoke's theorem to evaluate  ...

Question 15

Find the work done by the force field   in moving an object along an arch of the cycloid

Accepted Answer

The answer of Find the work done by the force...

Question 16

Select the correct Answer for each question.
-Find the work done by the force field F on a particle that moves along the curve C.

Accepted Answer

A) 17 
B) 19 
C) 34 
D)    
A) 17 
B) 19 
C) 34 
D)

Question 17

Select the correct Answer for each question.
-Find the exact mass of a thin wire in the shape of the helix   if the density is 5.

Accepted Answer

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

Question 18

Find a function   such that   and use it to evaluate   along the given curve C.   C is the upper semicircle that starts at (1, 2) and ends at (5, 2).

Accepted Answer

The answer of Find a function   such that...

Question 19

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

Accepted Answer

The answer of Determine whether F is conservative.If so, find...

Question 20

Select the correct Answer for each question.
-Show that F is conservative, and find a function f such that   and use the result to evaluate   where C is any curve from

Accepted Answer

A) -89 
B) 0 
C) -154 
D) -107 
A) -89 
B) 0 
C) -154 
D) -107

Show that F is conservative and find a function f such that and use this result to evaluate where C is any path from

Select the correct Answer for each question. -Use Green's Theorem to evaluate the line integral along the positively oriented closed curve where C is the triangle with vertices

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

Use a computer algebra system to compute the flux of F across S.S is the surface of the cube cut from the first octant by the planes Select the correct Answer

Find the work done by the force field F on a particle that moves along the curve C.Select the correct Answer

Use the Divergence Theorem to calculate the surface integral that is, calculate the flux of across . S is the surface of the box bounded by the coordinate planes and the planes Select the correct Answer

Use Stoke's theorem to evaluate C is the curve of intersection of the hyperbolic paraboloid and the cylinder oriented counterclockwise as viewed from above.

Find a parametric representation for the part of the plane that lies inside the cylinder

Use Stoke's theorem to evaluate and C is the boundary of the part of the plane in the first octant.Select the correct Answer

Select the correct Answer for each question. -Evaluate S is the part of the torus with vector representation

Use Stoke's theorem to evaluate C is the curve of intersection of the plane and the cylinder

Find the area of the surface.The part of the paraboloid ; ,

Determine whether or not F is a conservative vector field.If it is, find a function such that

Use Stoke's theorem to evaluate C is the curve of intersection of the hyperbolic paraboloid and the cylinder oriented counterclockwise as viewed from above.

Find the work done by the force field in moving an object along an arch of the cycloid

Select the correct Answer for each question. -Find the work done by the force field F on a particle that moves along the curve C.

Select the correct Answer for each question. -Find the exact mass of a thin wire in the shape of the helix if the density is 5.

Find a function such that and use it to evaluate along the given curve C. C is the upper semicircle that starts at (1, 2) and ends at (5, 2).

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

Select the correct Answer for each question. -Show that F is conservative, and find a function f such that and use the result to evaluate where C is any curve from

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Second-Order Differential Equations

Filters

Exam 16: Vector Calculus

Show that F is conservative and find a function f such that and use this result to evaluate where C is any path from

Select the correct Answer for each question. -Use Green's Theorem to evaluate the line integral along the positively oriented closed curve where C is the triangle with vertices

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

Use a computer algebra system to compute the flux of F across S.S is the surface of the cube cut from the first octant by the planes Select the correct Answer

Find the work done by the force field F on a particle that moves along the curve C.Select the correct Answer

Use the Divergence Theorem to calculate the surface integral that is, calculate the flux of across . S is the surface of the box bounded by the coordinate planes and the planes Select the correct Answer

Use Stoke's theorem to evaluate C is the curve of intersection of the hyperbolic paraboloid and the cylinder oriented counterclockwise as viewed from above.

Find a parametric representation for the part of the plane that lies inside the cylinder

Use Stoke's theorem to evaluate and C is the boundary of the part of the plane in the first octant.Select the correct Answer

Select the correct Answer for each question. -Evaluate S is the part of the torus with vector representation

Use Stoke's theorem to evaluate C is the curve of intersection of the plane and the cylinder

Find the area of the surface.The part of the paraboloid ; ,

Determine whether or not F is a conservative vector field.If it is, find a function such that

Use Stoke's theorem to evaluate C is the curve of intersection of the hyperbolic paraboloid and the cylinder oriented counterclockwise as viewed from above.

Find the work done by the force field in moving an object along an arch of the cycloid

Select the correct Answer for each question. -Find the work done by the force field F on a particle that moves along the curve C.

Select the correct Answer for each question. -Find the exact mass of a thin wire in the shape of the helix if the density is 5.

Find a function such that and use it to evaluate along the given curve C. C is the upper semicircle that starts at (1, 2) and ends at (5, 2).

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

Select the correct Answer for each question. -Show that F is conservative, and find a function f such that and use the result to evaluate where C is any curve from

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Second-Order Differential Equations

Filters