Calculus 3    Hour Exam 3  (continued)    -  Math 241    Fall, 2010

 

 

5a.

 

 

State what it means for a vector field,  F,  to be incompressible.

                                  

Answer:   div (  F  )  =  0

 

 

 

5b.

 

Is  the vector field,   F  =   f(y,z) i  +  g(x,z)  j  +  h(x,y) k  incompressible.  

Justify your answer.

 

Answer:  Yes

 

 

 

 

 

 

 

 

 

5c.

 

 

Compute the value of   ∫ ydx  +  x dy  where the path,  C,  is as follows:

 

 

 

  Answer:  0