(4.xz, y², yz) over the surface of the cube defined by the set of (x, y, z) satisfying 0

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(4.xz, y², yz) over the surface of<br>the cube defined by the set of (x, y, z) satisfying 0 < x < 1, 0 < y< 1, 0 < z < 1.<br>1. (a) Verify the divergence theorem for the vector field F=<br>(b) Evaluate the surface integral f f,F· ndS, where F(x,y, z) = (1, 1, z(x² +y²)²) and S<br>is the surface of the cylinder x2 + y? < 1, 0 < z < 1, including the sides and both lids.<br>

Extracted text: (4.xz, y², yz) over the surface of the cube defined by the set of (x, y, z) satisfying 0 < x="">< 1,="" 0=""><>< 1,="" 0="">< z="">< 1.="" 1.="" (a)="" verify="" the="" divergence="" theorem="" for="" the="" vector="" field="" f="(b)" evaluate="" the="" surface="" integral="" f="" f,f·="" nds,="" where="" f(x,y,="" z)="(1," 1,="" z(x²="" +y²)²)="" and="" s="" is="" the="" surface="" of="" the="" cylinder="" x2="" +="" y?="">< 1,="" 0="">< z="">< 1,="" including="" the="" sides="" and="" both="">

Jun 05, 2022

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(4.xz, y², yz) over the surface of the cube defined by the set of (x, y, z) satisfying 0

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