Divergence and Curl of a Vector Field

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1. Consider the vector field v(x,y,z)=(x2,-yx,z-xz).
(a) Compute the divergence and curl of v.
(b) Show that v is neither the gradient of a function nor the curl of a C2 vector field.

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We have:

Thus, the divergence is:

While the curl is:

We recall that the order of ...