Question 1

Evaluate   where   and C is any positively oriented simple closed curve enclosing the origin.

Accepted Answer

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

Question 2

Find the divergence of   .

Accepted Answer

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

Question 3

Determine whether   is conservative and/or incompressible.

Accepted Answer

A)  conservative and incompressible 
B)  conservative and compressible 
C)  not conservative and incompressible 
D)  not conservative and compressible 
A)  conservative and incompressible 
B)  conservative and compressible 
C)  not conservative and incompressible 
D)  not conservative and compressible

Question 4

Use the Divergence Theorem to set up and evaluate a triple integral for computing the outward flux of F over   where Q is bounded by   and   and   .

Accepted Answer

The answer of Use the Divergence Theorem to set up...

Question 5

Find the outward flux of F over   where Q is bounded by   and   and   .

Accepted Answer

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

Question 6

Determine if   is conservative, and if so, find a potential function   of the vector field.

Accepted Answer

A)    is conservative with   
B)    is conservative with   
C)    is conservative with   
D)    is not conservative 
A)    is conservative with   
B)    is conservative with   
C)    is conservative with   
D)    is not conservative

Question 7

Use Stokes' Theorem to compute   for   and C is the boundary of the portion of the paraboloid   with   and with   to the right.

Accepted Answer

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

Evaluate where and C is any positively oriented simple closed curve enclosing the origin.

Find the divergence of .

Determine whether is conservative and/or incompressible.

Use the Divergence Theorem to set up and evaluate a triple integral for computing the outward flux of F over where Q is bounded by and and .

Find the outward flux of F over where Q is bounded by and and .

Determine if is conservative, and if so, find a potential function of the vector field.

Use Stokes' Theorem to compute for and C is the boundary of the portion of the paraboloid with and with to the right.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Second Order Differential Equations

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Exam 16: Vector Calculus