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If F(x,y,z) is continuous and
for all (x,y,z), show that R3
dot F dV = 0

I have been working on this problem all day, and I'm honestly not sure how to proceed. The hint given on this problem is, "Take B

I have been working on this problem all day, and I'm honestly not sure how to proceed. The hint given on this problem is, "Take B

_{r to be a ball of radius r centered at the origin, apply divergence theorem, and let the radius tend to infinity." I tried letting F = 1/((x2 +y2+z2)(3/2))+1), and taking the divergence of that, but it didn't really seem to get me anywhere. If anyone has any suggestions for at least how to set up this proof, I would really appreciate it.}
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