# Key Section 1 Quiz 6.1-6.3 Part 2

MVC Chapter 6 Quiz NAME:

I nstructions: SHOW ALL WORK !! Calculator allowed, but all set up must be shown in order to gat full credit. Explain how and when you use calculator.

1. a. Determine a scalar potential for vector field F

 x

 xy

2 i y 2

 x

2 

1 j y 3

. f x

 x

 y

2 xy

2

 y x

2 x ( , )

2 x y

2

2 x

2

 

2

, f y

  x

2 

1

 

1 y

3 y

3

( x

2 

1)

  x

2 y

2

2

1

2 y

2

 

2 x y

2

2

 x

2

2 2

1 y

2

C b. Find the work done by from (0,1) to (1,1).

F in moving a particle along the parabolic path y 1 x x

2

C

F d s

C

( )

 d s

 f (1,1)

 f (0,1)

3 1

2 2

1

C c. Can the Fundamental Theorem of line integrals be used to calculate x

 xy

2 y

2 dx

 x

2 

1 dy y

3 for a path from (1,1) to (1, 1) . Explain briefly .

NO. Any path from (1,1) to (1, 1) crosses the x-axes and hence will contain a point with y = 0.

Therefore the vector field F will not be conservative on an open set containing the path.

MVC