Question 1

Let  where  .Which of the following equations does the line segment from  to  satisy?

Accepted Answer

A)   
B)   
C)  none of these B

Question 2

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 property of vector fields, not scalar fields. So, curl f is not meaningful.

Question 3

Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone  if its density function is

Accepted Answer

The answer of Find the moment of inertia about the...

Question 4

A particle is moving in a velocity field  At time t = 1 the particle is located at the point (1, 5, 5).a). What is the velocity of the particle at t = 1?
b). What is the approximate location of the particle at t = 1.01?

Accepted Answer

The answer of A particle is moving in a velocity...

Question 5

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

Accepted Answer

A)  4
B)  1
C)  3
D)   
E)  0.67

Question 6

Use Stokes' Theorem to evaluate    is the part of the paraboloid  that lies inside the cylinder  oriented upword.

Accepted Answer

A)  2
B)   
C)  4
D)  3
E)  1

Question 7

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 8

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Evaluate  where C is the right half of the circle

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Use Stokes' Theorem to evaluate  where  and  is the triangle with vertices   is oriented counterclockwise as viewed from above.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Which plot illustrates the vector field

Accepted Answer

A)   
B)   
C)   
D)

Question 13

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...

Question 14

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)  0
B)   
C)   
D)   
E)

Question 15

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)    + e
C)   
D)

Question 16

Evaluate the surface integral.  S is the part of the plane  that lies in the first octant.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

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 18

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

A)   
B)   
C)   
D)   
E)

Question 19

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 20

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 13: Vector Calculus

Let where .Which of the following equations does the line segment from to satisy?

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 the moment of inertia about the z-axis of a thin funnel in the shape of a cone if its density function is

A particle is moving in a velocity field At time t = 1 the particle is located at the point (1, 5, 5).a). What is the velocity of the particle at t = 1? b). What is the approximate location of the particle at t = 1.01?

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

Use Stokes' Theorem to evaluate is the part of the paraboloid that lies inside the cylinder oriented upword.

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

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

Evaluate where C is the right half of the circle

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

Use Stokes' Theorem to evaluate where and is the triangle with vertices is oriented counterclockwise as viewed from above.

Which plot illustrates the vector field

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 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 .

Evaluate the surface integral. S is the part of the plane that lies in the first octant.

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

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

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