(915, #25) From a plot of

guess whether it is conservative. Then determine whether your guess is correct.

Solution: Here is a plot of F

F does not appear to be conservative. If we were to draw a counterclockwise closed curve around the point ( 2, 1 ), where F = 0,

then the field vectors go in the same direction as the tangents to the path we are following. None of the field vectors go in the opposite direction of each other. Therefore along this path

so the field not conservative.

To verify this, assume F = <P,Q> is conservative, so F = < f_x, f_y> for some F. Then:

Therefore the vector field is not conservative.

By C.A.H.