Verify the Divergence Theorem for (mathbf{F}(x, y, z)=langle 0,0, zangle) and the region (x^{2}+y^{2}+z^{2}=1). THEOREM 1 Divergence

Verify the Divergence Theorem for \(\mathbf{F}(x, y, z)=\langle 0,0, zangle\) and the region \(x^{2}+y^{2}+z^{2}=1\).

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THEOREM 1 Divergence Theorem Let S be a closed surface that encloses a region W in R. Assume that S is piecewise smooth and is oriented by normal vectors pointing to the outside of W. If F is a vector field whose components have continuous partial derivatives in an open domain containing W, then div(F) dv J.P. = ffw F-dS=