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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