010.102-2005-2-fin - o ӧ 2 eK > 2005 12 10{ 13r 15r...

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Unformatted text preview: o ӧ 2 eK > 2005 12 10{ 13r 15r 4 Z 9 < : s2: %V IU lǣ k k( 200). M K+ c a Z @\ \ 1. (30&) 6 &` #. h h r (a) (b) 1 1 y sin(y 3 ) dy dx 0 x 1 1 1 + y 3 dy dx 0 x 2. (20&) %% D : 0 y x, 1 x2 + y 2 4 \ @ # G : D R2 (u, v) = G(x, y) = h i / 2 2 (x - y , 2xy) #4 e . QR 6 y 6\ #. t (a) det(G ) ` #. (b) G(D) _ x (u, v) = 9< 1 u2 +v 2 #| M G(D) _ ||` #. Q9 : 9 Ӧ 3. 4. (20&) 6 &` #. h h r C (x cosh(2y)) dx + (2x2 sinh(2y)) dy , C : y = x y = x2 _ > < Q t r (20&) D(2) = {(x, y) R2 |x2 + y 2 4} [-2, 2] [-2, 2] z` s6 # 6 1 h p H x x x d` 7" #. 2 x2 1 1 e- 2 dx 1 - 2 ( 0.93) e 2 -2 (30&) 6 / S_ Vs d` #. h B ,< G S = {(x, y, z)|x2 + y 2 + z 2 = a2 , z x2 + y 2 } 5. 6. (30&) 0 u 2, 0 v 2, 0 < < \ @ # / X 6 s B>% h / B G ho&3 . X(u, v) = ( cos u + cos u cos v, sin u + sin u cos v, sin v) (a) u0 = v0 = 2 9: {M, X(u0 , v0 ) \"_ ]_ ~&d` #. f X (b) /_ Vs\ #. G B , 7. (30&) h x 1 h r (a) &o\ s6 # & (xez + y sin x + z 2 ) dS R f AB \ #. #l" R 0/ x2 + y 2 + z 2 1 s. r N (b) 7' F (x, y, z) = (x, y, z 2 ) s z = x2 +y 2 (0 z 1) ` 4 (flux)` t R H #. sM ` & 0Z7' n n k 0 s 2 #. : AO Ӧ H r & Q 8. (20&) " z = h x2 + y 2 y + 2z = 2 /` C . H G B (a) C \ xy &% / Cp \ x, y \ d #. B G a (b) Cp s r> ~s 2 C _ #&` M, & _ & s Q : h r -y dx + x dy + z 3 dz C \ #. ...
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