Question 1

Select the correct Answer for each question.
-Find the correct identity, if f is a scalar field, F and G are vector fields.

Accepted Answer

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

Question 2

Select the correct Answer for each question.
-Evaluate the line integral over the given curve C.

Accepted Answer

A) 28 
B)    
C)    
D)    
A) 28 
B)    
C)    
D)

Question 3

Find the mass of the surface S having the given mass density.S is the hemisphere   the density at a point P on S is equal to the distance between P and the xy-plane.Select the correct Answer

Accepted Answer

A)    
B)    
C) 64 
D)    
A)    
B)    
C) 64 
D)

Question 4

Match the equation with one of the graphs below.

Accepted Answer

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

Question 5

Select the correct Answer for each question.
-Use Stokes' Theorem to evaluate     C is the curve obtained by intersecting the cylinder   with the hyperbolic paraboloid   oriented in a counterclockwise direction when viewed from above

Accepted Answer

A)    
B) 0 
C)    
D) 1 
A)    
B) 0 
C)    
D) 1

Question 6

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 7

Select the correct Answer

Accepted Answer

A) 6 
B) 12 
C) 18 
D) 30 
E) None of these 
A) 6 
B) 12 
C) 18 
D) 30 
E) None of these

Question 8

Find the divergence of the vector field F.   Select the correct Answer

Accepted Answer

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

Question 9

Evaluate the line integral over the given curve C.

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and
components of the vector fields have continuous second order partial derivatives, find   where a is the constant vector.

Accepted Answer

The answer of Assuming that S satisfies the conditions of...

Question 12

Evaluate     S is the part of the torus with vector representation   Select the correct Answer

Accepted Answer

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

Question 13

Select the correct Answer for each question.
-Find the area of the surface.The part of the paraboloid

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

The answer of Use the Divergence Theorem to calculate the...

Question 16

Find the curl of the vector field F.

Accepted Answer

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

Question 17

Find the gradient vector field of

Accepted Answer

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

Question 18

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 19

Select the correct Answer for each question.
-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

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

Question 20

Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere   Select the correct Answer

Accepted Answer

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

Select the correct Answer for each question. -Find the correct identity, if f is a scalar field, F and G are vector fields.

Select the correct Answer for each question. -Evaluate the line integral over the given curve C.

Find the mass of the surface S having the given mass density.S is the hemisphere the density at a point P on S is equal to the distance between P and the xy-plane.Select the correct Answer

Match the equation with one of the graphs below.

Select the correct Answer for each question. -Use Stokes' Theorem to evaluate C is the curve obtained by intersecting the cylinder with the hyperbolic paraboloid oriented in a counterclockwise direction when viewed from above

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

Select the correct Answer

Find the divergence of the vector field F. Select the correct Answer

Evaluate the line integral over the given curve C.

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

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find where a is the constant vector.

Evaluate S is the part of the torus with vector representation Select the correct Answer

Select the correct Answer for each question. -Find the area of the surface.The part of the paraboloid

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

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

Find the curl of the vector field F.

Find the gradient vector field of

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

Suppose that where g is a function of one variable such that Evaluate where S is the sphere Select the correct Answer

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

Select the correct Answer for each question. -Find the correct identity, if f is a scalar field, F and G are vector fields.

Select the correct Answer for each question. -Evaluate the line integral over the given curve C.

Find the mass of the surface S having the given mass density.S is the hemisphere the density at a point P on S is equal to the distance between P and the xy-plane.Select the correct Answer

Match the equation with one of the graphs below.

Select the correct Answer for each question. -Use Stokes' Theorem to evaluate C is the curve obtained by intersecting the cylinder with the hyperbolic paraboloid oriented in a counterclockwise direction when viewed from above

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

Select the correct Answer

Find the divergence of the vector field F. Select the correct Answer

Evaluate the line integral over the given curve C.

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

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find where a is the constant vector.

Evaluate S is the part of the torus with vector representation Select the correct Answer

Select the correct Answer for each question. -Find the area of the surface.The part of the paraboloid

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

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

Find the curl of the vector field F.

Find the gradient vector field of

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

Suppose that where g is a function of one variable such that Evaluate where S is the sphere Select the correct Answer

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