Question 1

Find the divergence at   for the vector field

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E)

Question 2

Evaluate the line integral along the given path.

Accepted Answer

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Question 3

Find the area of the lateral surface over the curve C in the xy-plane and under the surface   where Lateral surface     line from

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E)

Question 4

Find the conservative vector field for the potential function   by finding its gradient.

Accepted Answer

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E)

Question 5

Find

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D)

Question 6

Find the divergence of the vector field at the given point.

Accepted Answer

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E)

Question 7

Sketch several representative vectors in the vector field given by

Accepted Answer

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E)

Question 8

Find the work done by a person weighing   pounds walking exactly one revolution up a circular helical staircase of radius   feet if the person rises   feet.

Accepted Answer

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Question 9

Evaluate   where C is represented by

Accepted Answer

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E)    
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Question 10

A tractor engine has a steel component with a circular base modeled by the vector- valued function   Its height is given by   (All measurements of the
Component are given in centimeters.) Find the lateral surface area of the component.Round your
Answer to two decimal places.

Accepted Answer

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

Question 11

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Accepted Answer

A) conservative with potential function   
B)    conservative with potential function 
C)    conservative with potential function 
D) conservative with potential function   
E) not conservative 
A) conservative with potential function   
B)    conservative with potential function 
C)    conservative with potential function 
D) conservative with potential function   
E) not conservative

Question 12

Compute   for the vector field given by

Accepted Answer

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

Question 13

Find the moments of inertia for a wire that lies along   with density

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find a piecewise smooth parametrization of the path C given in the following graph.

Accepted Answer

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

Find the divergence at for the vector field

Evaluate the line integral along the given path.

Find the area of the lateral surface over the curve C in the xy-plane and under the surface where Lateral surface line from

Find the conservative vector field for the potential function by finding its gradient.

Find

Find the divergence of the vector field at the given point.

Sketch several representative vectors in the vector field given by

Find the work done by a person weighing pounds walking exactly one revolution up a circular helical staircase of radius feet if the person rises feet.

Evaluate where C is represented by

A tractor engine has a steel component with a circular base modeled by the vector- valued function Its height is given by (All measurements of the Component are given in centimeters.) Find the lateral surface area of the component.Round your Answer to two decimal places.

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Compute for the vector field given by

Find the moments of inertia for a wire that lies along with density

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

Find a piecewise smooth parametrization of the path C given in the following graph.

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Additional Topics in Differential Equations

Preparation for Calculus

Filters

Exam 15: Vector Analysis

Find the divergence at for the vector field

Evaluate the line integral along the given path.

Find the area of the lateral surface over the curve C in the xy-plane and under the surface where Lateral surface line from

Find the conservative vector field for the potential function by finding its gradient.

Find

Find the divergence of the vector field at the given point.

Sketch several representative vectors in the vector field given by

Find the work done by a person weighing pounds walking exactly one revolution up a circular helical staircase of radius feet if the person rises feet.

Evaluate where C is represented by

A tractor engine has a steel component with a circular base modeled by the vector- valued function Its height is given by (All measurements of the Component are given in centimeters.) Find the lateral surface area of the component.Round your Answer to two decimal places.

Determine whether the vector field is conservative.If it is, find a potential function for the vector field.

Compute for the vector field given by

Find the moments of inertia for a wire that lies along with density

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

Find a piecewise smooth parametrization of the path C given in the following graph.

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Additional Topics in Differential Equations

Preparation for Calculus

Filters