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QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the par...

QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric r

QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f, F.n ds, where (d) 1 Fxi-yzjz2k. 2 (9 marks)
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(a) r(z,e)= (2cos ,2 sin 6,2) (b) (-2 cos )-(2sin e) +k (0-0) 0 0 1 rxr 2 sin 2 cos 0 x2 (e) 2 3 (2dz (2sin 1+-yz 8 1+ 0 0 2z

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QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the par...
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