Question 1

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 2

Find the area of the surface S where S is the part of the surface   that lies inside the cylinder

Accepted Answer

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

Question 3

Let f 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 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 curl of the vector field.

Accepted Answer

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

Question 6

The flow lines (or streamlines)of a vector field are the paths followed by a particle whose velocity field is the given vector field.Thus,the vectors in a vector field are tangent to the flow lines.The flow lines of the vector field   satisfy the differential equations   and   Solve these differential equations to find the equations of the family of flow lines.

Accepted Answer

The answer of The flow lines (or streamlines)of a vector...

Question 7

Use Gauss's Law to find the charge contained in the solid hemisphere   ,if the electric field is

Accepted Answer

The answer of Use Gauss's Law to find the charge...

Question 8

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

Accepted Answer

The curl is a proper

Question 9

Find an equation of the tangent plane to the parametric surface represented by r at the specified point.   ;

Accepted Answer

The answer of Find an equation of the tangent plane...

Question 10

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),(   ,0)and (0,   ).

Accepted Answer

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

Question 11

Which plot illustrates the vector field

Accepted Answer

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D)

Question 12

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 13

Use Stokes' Theorem to evaluate   where     is the circle   .   is oriented counterclockwise as viewed from above.

Accepted Answer

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E)    
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E)

Question 14

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

Accepted Answer

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

Question 15

Evaluate the line integral over the given curve C.   ;   ,

Accepted Answer

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

Question 16

Find (a)the divergence and (b)the curl of the vector field F.

Accepted Answer

The answer of Find (a)the divergence and (b)the curl of...

Question 17

Evaluate   where C is the right half of the circle

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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   .

Accepted Answer

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

Question 20

Find the divergence of the vector field.

Accepted Answer

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

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

Find the area of the surface S where S is the part of the surface that lies inside the cylinder

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

Find the gradient vector field of

Find the curl of the vector field.

Use Gauss's Law to find the charge contained in the solid hemisphere ,if the electric field is

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

Find an equation of the tangent plane to the parametric surface represented by r at the specified point. ;

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),( ,0)and (0, ).

Which plot illustrates the vector field

Suppose that where g is a function of one variable such that . Evaluate where S is the sphere

Use Stokes' Theorem to evaluate where is the circle . is oriented counterclockwise as viewed from above.

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

Evaluate the line integral over the given curve C. ; ,

Find (a)the divergence and (b)the curl of the vector field F.

Evaluate where C is the right half of the circle

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

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 .

Find the divergence of the vector field.

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Exam 13: Vector Calculus

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

Find the area of the surface S where S is the part of the surface that lies inside the cylinder

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

Find the gradient vector field of

Find the curl of the vector field.

Use Gauss's Law to find the charge contained in the solid hemisphere ,if the electric field is

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

Find an equation of the tangent plane to the parametric surface represented by r at the specified point. ;

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),( ,0)and (0, ).

Which plot illustrates the vector field

Suppose that where g is a function of one variable such that . Evaluate where S is the sphere

Use Stokes' Theorem to evaluate where is the circle . is oriented counterclockwise as viewed from above.

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

Evaluate the line integral over the given curve C. ; ,

Find (a)the divergence and (b)the curl of the vector field F.

Evaluate where C is the right half of the circle

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

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 .

Find the divergence of the vector field.

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