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Homework Statement:

Which of the following is the divergence of the vector field shown (see attachment for visual)?
f(x,y)=
a) x
b) y
c) x
d) y
e) x+y
f) xy
g) yx
h) yx
Relevant Equations:

div(f) = d/dx f1 + d/dy f2 + d/dz f3
scalar curl of f = d f2/dx  d f1/dy
For divergence: We learned to draw a circle at different locations and to see if gas is expanding/contracting. Whenever the ycoordinate is positive, the gas seems to be expanding, and it's contracting when negative. I find it hard to tell if the gas is expanding or contracting as I go to the right and left, so I'm not sure what xdependence it has. It seems like it's symmetrical, so perhaps no xdependence and f(x,y)=y?
For curl, I'm kind of confused. I thought scalar curl had to do with rotation. But some examples the teacher gives just has straight lines (doesn't seem to be rotation) and there is a nonzero scalar curl. It does seem to be rotating clockwise on the right side and counterclockwise on the left, so does that just mean it's equal to x?
I'm struggling for better intuition here and not sure if I'm just reaching.
For curl, I'm kind of confused. I thought scalar curl had to do with rotation. But some examples the teacher gives just has straight lines (doesn't seem to be rotation) and there is a nonzero scalar curl. It does seem to be rotating clockwise on the right side and counterclockwise on the left, so does that just mean it's equal to x?
I'm struggling for better intuition here and not sure if I'm just reaching.
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