Question 1

Select the correct Answer for each question.
-Evaluate for the vector field F and the path C.(Hint: Show that F is conservative, and pick a simpler path.)

Accepted Answer

A) 24 
B) 47 
C) 0 
D)    
A) 24 
B) 47 
C) 0 
D)

Question 2

Select the correct Answer for each question.
-Use Green's Theorem to find the work done by the force   in moving a particle in the positive direction once around the triangle with vertices

Accepted Answer

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

Question 3

Find the curl of the vector field.   Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 4

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C.   where C is the triangle with vertices

Accepted Answer

The answer of Use Green's Theorem to evaluate the line...

Question 5

Select the correct Answer for each question.
-Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 6

Find the curl of the vector field F.

Accepted Answer

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

Question 7

Select the correct Answer for each question.
-A plane lamina with constant density   occupies a region in the xy-plane bounded by a simple closed path C.Its moments of inertia about the axes are   Find the moments of inertia about the axes, if C is a rectangle with vertices (0, 0), (4, 0), (4, 5) and

Accepted Answer

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

Question 8

Let D be a region bounded by a simple closed path C in the xy.Then the coordinates of the centroid   where A is the area of D.Find the centroid of the triangle with vertices (0, 0),

Accepted Answer

The answer of Let D be a region bounded by...

Question 9

where   S consists of the hemisphere   and the disk   in the   Select the correct Answer 
a.   
b.   
c.   
d.   
e.

Accepted Answer

The answer of   where   S consists...

Question 10

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

Accepted Answer

The answer of Determine whether or not vector field is...

Question 11

Let   be a scalar field.Determine whether the expression is meaningful.If so, state whether the expression represents a scalar field or a vector field.

Accepted Answer

The vector grad f is defined.I

Question 12

A thin wire in the shape of a quarter-circle   has a linear mass density   Find the mass and the location of the center of mass of the wire.

Accepted Answer

The answer of A thin wire in the shape of...

Question 13

Select the correct Answer for each question.
-Let D be a region bounded by a simple closed path C in the xy.Then the coordinates of the centroid   where A is the area of D.Find the centroid of the triangle with vertices (0, 0),   and (0,

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Evaluate the line integral over the given curve C.   where C is the line segment joining

Accepted Answer

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

Question 16

Select the correct Answer for each question.
-Find the curl of the vector field F.

Accepted Answer

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

Question 17

Match the equation with one of the graphs below.

Accepted Answer

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

Question 18

Find the curl of

Accepted Answer

The answer of Find the curl of  ...

Question 19

Select the correct Answer for each question.
-Let S be the cube with vertices   Approximate   by using a Riemann sum as in Definition 1, taking the patches   to be the squares that are the faces of the cube and the points   to be the centers of the squares.

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Question 20

Let S be the cube with vertices   Approximate   by using a Riemann sum as in Definition 1, taking the patches   to be the squares that are the faces of the cube and the points   to be the centers of the squares.

Accepted Answer

The answer of Let S be the cube with vertices...

Select the correct Answer for each question. -Evaluate for the vector field F and the path C.(Hint: Show that F is conservative, and pick a simpler path.)

Select the correct Answer for each question. -Use Green's Theorem to find the work done by the force in moving a particle in the positive direction once around the triangle with vertices

Find the curl of the vector field. Select the correct Answer

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. where C is the triangle with vertices

Select the correct Answer for each question. -Suppose that where g is a function of one variable such that Evaluate where S is the sphere

Find the curl of the vector field F.

Select the correct Answer for each question. -A plane lamina with constant density occupies a region in the xy-plane bounded by a simple closed path C.Its moments of inertia about the axes are Find the moments of inertia about the axes, if C is a rectangle with vertices (0, 0), (4, 0), (4, 5) and

Let D be a region bounded by a simple closed path C in the xy.Then the coordinates of the centroid where A is the area of D.Find the centroid of the triangle with vertices (0, 0),

where S consists of the hemisphere and the disk in the Select the correct Answer a. b. c. d. e.

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

Let be a scalar field.Determine whether the expression is meaningful.If so, state whether the expression represents a scalar field or a vector field.

A thin wire in the shape of a quarter-circle has a linear mass density Find the mass and the location of the center of mass of the wire.

Select the correct Answer for each question. -Let D be a region bounded by a simple closed path C in the xy.Then the coordinates of the centroid where A is the area of D.Find the centroid of the triangle with vertices (0, 0), and (0,

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

Evaluate the line integral over the given curve C. where C is the line segment joining

Select the correct Answer for each question. -Find the curl of the vector field F.

Match the equation with one of the graphs below.

Find the curl of

Select the correct Answer for each question. -Let S be the cube with vertices Approximate by using a Riemann sum as in Definition 1, taking the patches to be the squares that are the faces of the cube and the points to be the centers of the squares.

Let S be the cube with vertices Approximate by using a Riemann sum as in Definition 1, taking the patches to be the squares that are the faces of the cube and the points to be the centers of the squares.

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Exam 16: Vector Calculus

Select the correct Answer for each question. -Evaluate for the vector field F and the path C.(Hint: Show that F is conservative, and pick a simpler path.)

Select the correct Answer for each question. -Use Green's Theorem to find the work done by the force in moving a particle in the positive direction once around the triangle with vertices

Find the curl of the vector field. Select the correct Answer

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. where C is the triangle with vertices

Select the correct Answer for each question. -Suppose that where g is a function of one variable such that Evaluate where S is the sphere

Find the curl of the vector field F.

Select the correct Answer for each question. -A plane lamina with constant density occupies a region in the xy-plane bounded by a simple closed path C.Its moments of inertia about the axes are Find the moments of inertia about the axes, if C is a rectangle with vertices (0, 0), (4, 0), (4, 5) and

Let D be a region bounded by a simple closed path C in the xy.Then the coordinates of the centroid where A is the area of D.Find the centroid of the triangle with vertices (0, 0),

where S consists of the hemisphere and the disk in the Select the correct Answer a. b. c. d. e.

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

Let be a scalar field.Determine whether the expression is meaningful.If so, state whether the expression represents a scalar field or a vector field.

A thin wire in the shape of a quarter-circle has a linear mass density Find the mass and the location of the center of mass of the wire.

Select the correct Answer for each question. -Let D be a region bounded by a simple closed path C in the xy.Then the coordinates of the centroid where A is the area of D.Find the centroid of the triangle with vertices (0, 0), and (0,

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

Evaluate the line integral over the given curve C. where C is the line segment joining

Select the correct Answer for each question. -Find the curl of the vector field F.

Match the equation with one of the graphs below.

Find the curl of

Select the correct Answer for each question. -Let S be the cube with vertices Approximate by using a Riemann sum as in Definition 1, taking the patches to be the squares that are the faces of the cube and the points to be the centers of the squares.

Let S be the cube with vertices Approximate by using a Riemann sum as in Definition 1, taking the patches to be the squares that are the faces of the cube and the points to be the centers of the squares.

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