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# 2009è€ƒç ”æ•°å­¦å¼ºåŒ–ç

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Unformatted text preview: www.etsinghua.org 010-62701055/82378805 B 503 x y = x ≥ a a x a a x ≤ ≤ − ⇔ ≤ = a = x a x a x a x − ≤ ≥ ⇔ ≥ x x x x x x 2 , ≤ + ≤ ≤ ≤ − R y x ∈ ∀ , y x y x + ≤ + y x y x − ≥ − R y x ∈ ∀ , xy y x ≥ + ) ( 2 2 2 1 ≥ ≥ y x , xy y x ≥ + ) ( 2 1 ) , [ 2 π ∈ x x x x tan sin ≤ ≤ R y x ∈ ∀ , ) cos( ) sin( ) cos( ) sin( y x y x y x y x − + + ≤ − − + y)- cos(x ) sin( y x + , , > ∀ k n m n m < k n k m n m + + < ) ( x f y = X X x x ∈ ∀ 2 1 , 2 1 x x < ) ( ) ( 2 1 x f x f ≤ ) ( x f y = X 2 1 x x < ) ( ) ( 2 1 x f x f < ) ( x f y = X 1 www.etsinghua.org 010-62701055/82378805 B 503 ) ( x f y = a x = ) ( ) ( x a f x a f + = − ) ( ) ( x a f x g − = ) ( ) ( ) ( ) ( x g x a f x a f x g = − = + = − ) ( x g ) ( x f y = ) , ( a ) ( ) ( x a f x a f + − = − ) ( ) ( x a f x g − = ) ( ) ( ) ( ) ( x g x a f x a f x g − = − − = + = − ) ( x g ) ( x f ) ( x f y = X M X x ∈ M x f ≤ ) ( ) ( x f y = X ) ( x f y = a x = ) ( ) ( x a f x a f + = − ) ( ) ( x a f x g − = ) ( ) ( ) ( ) ( x g x a f x a f x g = − = + = − ) ( x g ) ( x f y = ) , ( a ) ( ) ( x a f x a f + − = − ) ( ) ( x a f x g − = ) ( ) ( ) ( ) ( x g x a f x a f x g − = − − = + = − ) ( x g ) ( x f ( ) x f y = ) , ( a ) , ( b b a < ( ) x f y = ᫓࿴ ) ( 2 a b T − = ᤰ ᧣ ṟᢶ ᢶ ) ( x f y = ) , ( a ) , ( b 2 www.etsinghua.org 010-62701055/82378805 B 503 ) ( ) ( x a f x a f + − = − ē ď Đ ᆉ t x a = − ē ᢶ ) ( ) ( t a f t f − − = 2 g 另៷ᠹᢶ ēჯሑ൱ᢶ ) ( ) ( x b f x b f + − = − ) ( ) ( t b f t f − − = 2 ē ᠵᙈᄌႯ ) ( ) ( t a f t b f − = − 2 2 ēᣂᮉᆉ u t a = − 2 ൱ᄌႯ )) ( ( ) ( a b u f u f − + = 2 ē Ả ē᫝᣾Ⴏ )) ( ( ) ( a b x f x f − + = 2 2 > − ) ( a b ēᖃᤎ ) ( x f y = ᫓࿴ᷣ ēᮁ᫓ ࿴ g ) ( a b T − = 2 ) ( x f y = ) ( • = f y )) ( ( x g f y = ) ( x g u = ) ( u f y = ) ( x g u = ) ( u f y = ) ( x f y = X Y Y y ∈ ∀ ) ( y g X x ∈ ) ( y g x = ) ( y g x = ) ( x f y = ) ( x f y = ) ( x f 1 − ) ( x g x x y = ) ( x f y = ) ( x g ) ( x f y = ) ( x g ) ( x f y = ) ( x g ) ( x f ) ( x g x x g f = )) ( ( x x f g = )) ( ( 3 www.etsinghua.org 010-62701055/82378805 B 503 ⎩ ⎨ ⎧ = = ) ( ) ( t y y t x x ) ( )) ( ( x f x t y y ∧ = = ⎪ ⎩ ⎪ ⎨ ⎧ > = < − = = , 1 , , 1 sgn ) ( x x x x x f x x e e x g − − − = 1 2 ) ( = )) ( ( x g f ) ( 1 2 = − = − − x x e e x g 3 1 = x x e y = ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ > = < − = 3 1 , 1 3 1 , 3 1 , 1 )) ( ( x x x x g f ⎩ ⎨ ⎧ > ≤ = , 1 , ) ( x x x f ⎩ ⎨ ⎧ + < ≤ + + + < ≤ = = 2 1 , 1 1 , ] [ ) ( n x n n n x n n x x f ] [ ) ( x x x f − = ) 2 , [ 4 www.etsinghua.org 010-62701055/82378805 B 503 ⎩ ⎨ ⎧ < ≤ − < ≤ = − = 2 1 , 1 1 , ] [ ) ( x x x x x x x f } , , 1 { max ) ( 3 2 2 x x x f x ≤ = } , , 1 { min ) ( 3 2 2 x x x f x ≤ = = ∫ − 2 2 3 2 } , , 1 max{ dx x x } , , 1 max{ 3 2 x x ⎪ ⎩ ⎪ ⎨ ⎧ > ≤ −...
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## This note was uploaded on 12/06/2011 for the course MATH Scatter taught by Professor Cheng during the Summer '10 term at Xiamen University.

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2009è€ƒç ”æ•°å­¦å¼ºåŒ–ç

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