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010-102-en-2002-2-final - > o 2(009-030 eK 1r 3r 4 Z 9<...

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Unformatted text preview: > o 2 (009-030) eK 2002 12 14{ 1r 3r 4 Z 9 < : s2: j h ]_ \ s&` "r r(8& 200&). HH x h 1. (30&) 6 4&_ ` . h h ͤr 1 1 y 5 y 0 (a) 0 e-x dxdy 3dxdy x2 + y 2 2 (b) 1 2. (30&) h (a) 7' F(x, y) = (2xyex y +3x2 , x2 ex y +cos y)_ F (x, y)\ < . (b) & X (2xyex y +3x2 )dx+(x2 ex y +cos y)dy\ . #l" X r h f H G B / y = x2 0_ (0, 0)\" (2, 4)t_ s. A f r 2 2 2 2 3. (20&) /\" 6 %%_ x\ . h aBf i N {(x, y, z) : x2 + y 2 z 2 - x2 - y 2 } 4. 5. Q , t r (20&) / x 3 + y 3 = 1 _ Vs\ . G h B (20&) C x = 0, y = 0, x + y = 1 y+_ Y\ r> h Q U t A t / ' B + : h @ ~ 3 /s M, 6 &` . H G r (x2 + y 2 )dx - 2xydy C 2 2 6. 7. (20&) 6 /_ Vs\ . h B , G {(x, y, z) : x2 + y 2 + z 2 = 4, x2 + y 2 2x, z 0} (20&) /_ %% R = {(x, y, z) | 1 4x2 + 9y 2 + 16z 2 4}\ @K N h B i / z 2 dxdydz (4x2 + 9y 2 + 16z 2 )3 R \ . 8. (20&) 6 &_ ` . h h r 3(x2 + y + z)dS, X S = {(x, y, z) | x2 + y 2 + z 2 = 1} (>_ _\ 0 # &o\ s6 # .) ߩ # A 1 x a 9. (20&) z = x2 + y 2 - 4 (-4 z 0)` 7' A(X) = h t R 4 ` . H X |X|3 ...
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