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010-102-en-2002-2-mid

# 010-102-en-2002-2-mid - > o 2(009-030 5 1r 3r 4 Z 9< s2...

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Unformatted text preview: > o 2 (009-030) 5 2002 10 26{ 1r 3r 4 Z 9 < : s2: j h ]_ \ s&` "r r(8& 200&). HH x h 1. 2 x y x2 + y 2 , f (x, y) = x4 + y 2 0, (a) (10&) f (x, y) "&\" 5? h H hf q (x, y) = (0, 0) (x, y) = (0, 0). (b) (10&) D1 f (0, 0) D2 f (0, 0)\ r. h < (c) (10&) "&\" f (x, y)_ p0\$` r. h hf p r x 2. 3. 4. 5. (20&) / 2y - z 3 - 3xz = 2 0_ &(1, 8, 2)\" ]` #. G h B A h f X ex (20&) g(x) = h < sin x 1 + y 3 dy\" f dg (0)\ #. dx (10&) F (x, y) = (xy, sin x, x2 y)_ q ' F (x, y)\ #. h < > = (20&) 6 /_ _ # & P \" s \ @ X_ h B Q h f / G ] ~&d` #. x3 + y 3 + z 3 - 3xyz = 4 < x3 - 2y 2 + z 2 = 3, P = (1, 1, 2). 6. (20&) 6 7' F (x, y)\" q '>d detF (1, 1)\ h < f = h ^& r. F (x, y) = (f1 (x, y), f2 (x, y)), f #l" f1 (x, y) = 1 cos(ux) du, f2 (x, y) = u 1 sin(vy) dvs. v 7. 8. 9. 10. (20&) f (x, y) = x y +1{ M, s _ _{ /\ (x-2) (y -2)_ h 9 : < 9Q L < L 4 & "/ r. (20&) f (x, y) = x3 + y 2 - 6xy + 6x + 3y_ [email protected]&, F&, & h < G/h Gh h ` #. (20&) x + 2y + z = 2\" f (x, y, z) = x2 + y 2 + z 2 _ ` h f j #. (20&) "&\" / z = xy + 1 t_ o\ r. h hf B G j 2 ...
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