Question 1

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

Accepted Answer

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

Question 2

The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical   Select the correct Answer

Accepted Answer

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

Question 3

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

Accepted Answer

The vector field @#IMG-DLM& is

Question 4

Find the gradient vector field of

Accepted Answer

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

Question 5

Find the gradient vector field of

Accepted Answer

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

Question 6

Find the gradient vector field of the scalar function f.(That is, find the conservative vector field F for the potential function f of F.)

Accepted Answer

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

Question 7

Select the correct Answer for each question.
-Use Green's Theorem and/or a computer algebra system to evaluate   where C is the circle   with counterclockwise orientation.

Accepted Answer

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

Question 8

Select the correct Answer for each question.
-Evaluate     S is the part of the plane   in the first octant.

Accepted Answer

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

Question 9

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   Select the correct Answer

Accepted Answer

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

Question 10

Below is given the plot of a vector field F in the xy-plane.(The z-component of F is 0.) By studying the plot, determine whether div F is positive, negative, or zero.

Accepted Answer

A) zero 
B) cannot be determined 
C) negative 
D) positive 
A) zero 
B) cannot be determined 
C) negative 
D) positive

Question 11

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 12

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

Accepted Answer

A) 224 
B) 135 
C) 117 
D) 70 
A) 224 
B) 135 
C) 117 
D) 70

Question 13

Let

Accepted Answer

The answer of Let    ...

Question 14

Match the vector field with its plot.Select the correct Answer

Accepted Answer

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

Question 15

Use Stokes' Theorem to evaluate     S is the part of the paraboloid   lying below the plane   and oriented with normal pointing downward.

Accepted Answer

The answer of Use Stokes' Theorem to evaluate  ...

Question 16

Which plot illustrates the vector field

Accepted Answer

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

Question 17

The plot of a vector field is shown below.A particle is moved   By inspection, determine whether the work done by F on the particle is positive, negative, or zero.

Accepted Answer

The answer of The plot of a vector field is...

Question 18

Select the correct Answer for each question.
-Find a parametric representation for the part of the elliptic paraboloid   that lies in front of the plane x = 0.

Accepted Answer

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

Question 19

A particle starts at the point   moves along the x-axis to (3, 0) and then along the semicircle   to the starting point.Use Green's Theorem to find the work done on this particle by the force field   Select the correct Answer

Accepted Answer

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

Question 20

Find a vector representation for the surface.The plane that passes through the point   and contains the vectors   and

Accepted Answer

The answer of Find a vector representation for the surface.The...

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

The temperature at the point in a substance with conductivity is Find the rate of heat flow inward across the cylindrical Select the correct Answer

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

Find the gradient vector field of

Find the gradient vector field of

Find the gradient vector field of the scalar function f.(That is, find the conservative vector field F for the potential function f of F.)

Select the correct Answer for each question. -Use Green's Theorem and/or a computer algebra system to evaluate where C is the circle with counterclockwise orientation.

Select the correct Answer for each question. -Evaluate S is the part of the plane in the first octant.

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 Select the correct Answer

Below is given the plot of a vector field F in the xy-plane.(The z-component of F is 0.) By studying the plot, determine whether div F is positive, negative, or zero.

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.

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

Let

Match the vector field with its plot.Select the correct Answer

Use Stokes' Theorem to evaluate S is the part of the paraboloid lying below the plane and oriented with normal pointing downward.

Which plot illustrates the vector field

The plot of a vector field is shown below.A particle is moved By inspection, determine whether the work done by F on the particle is positive, negative, or zero.

Select the correct Answer for each question. -Find a parametric representation for the part of the elliptic paraboloid that lies in front of the plane x = 0.

A particle starts at the point moves along the x-axis to (3, 0) and then along the semicircle to the starting point.Use Green's Theorem to find the work done on this particle by the force field Select the correct Answer

Find a vector representation for the surface.The plane that passes through the point and contains the vectors and

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Exam 16: Vector Calculus

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

The temperature at the point in a substance with conductivity is Find the rate of heat flow inward across the cylindrical Select the correct Answer

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

Find the gradient vector field of

Find the gradient vector field of

Find the gradient vector field of the scalar function f.(That is, find the conservative vector field F for the potential function f of F.)

Select the correct Answer for each question. -Use Green's Theorem and/or a computer algebra system to evaluate where C is the circle with counterclockwise orientation.

Select the correct Answer for each question. -Evaluate S is the part of the plane in the first octant.

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 Select the correct Answer

Below is given the plot of a vector field F in the xy-plane.(The z-component of F is 0.) By studying the plot, determine whether div F is positive, negative, or zero.

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.

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

Let

Match the vector field with its plot.Select the correct Answer

Use Stokes' Theorem to evaluate S is the part of the paraboloid lying below the plane and oriented with normal pointing downward.

Which plot illustrates the vector field

The plot of a vector field is shown below.A particle is moved By inspection, determine whether the work done by F on the particle is positive, negative, or zero.

Select the correct Answer for each question. -Find a parametric representation for the part of the elliptic paraboloid that lies in front of the plane x = 0.

A particle starts at the point moves along the x-axis to (3, 0) and then along the semicircle to the starting point.Use Green's Theorem to find the work done on this particle by the force field Select the correct Answer

Find a vector representation for the surface.The plane that passes through the point and contains the vectors and

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