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2009&egrave;€ƒ&ccedil;&nbsp;”&aelig;•&deg;&aring;&shy;&brvbar;&aring;&frac14;&ordm;&aring;Œ–&ccedil;

# 2009è€ƒç ”æ•°å­¦å¼ºåŒ–ç

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Unformatted text preview: www.etsinghua.org 010-62701055/82378805 B 503 1 1 1 ) ( x f ) ( ' > f > δ ) ( x f ) , ( δ ) ( x f ) , ( δ − ) , ( δ ∈ x ) ( ) ( f x f > ) , ( δ − ∈ x ) ( ) ( f x f > ) ( ) ( lim ) ( > − − = ′ → x f x f f x > δ ) , ( δ − ∈ x ) , ( δ ∈ x ) ( ) ( > − − x f x f ) ( ) ( f x f − x ) , ( δ ∈ x ) ( ) ( f x f > ) , ( δ − ∈ x ) ( ) ( f x f < ) ( x f = x 1 cos 1 ) ( lim = − ′ ′ → x x f x x ) ( ≠ ′ ′ f )) ( , ( f ) ( x f y = ) ( = ′ ′ f ) ( f ) ( x f ) ( = ′ ′ f )) ( , ( f ) ( x f y = ) ( ≠ ′ ′ f ) ( f ) ( x f 1 ) ( 2 lim cos 1 ) ( lim ≠ = ′ ′ = − ′ ′ → → x x f x x f x x x ) ( lim = ′ ′ → x f x 1 www.etsinghua.org 010-62701055/82378805 B 503 ) ( x f = x ) ( = ′ ′ f 1 ) ( 2 lim cos 1 ) ( lim > = ′ ′ = − ′ ′ → → x x f x x f x x x x ) ( 2 > ′ ′ x x f < x ) ( < ′ ′ x f > x ) ( > ′ ′ x f ) ( x f ′ ′ = x )) ( , ( f ) ( x f y = ) ( x f ] , [ b a ) ( ) ( = = b f a f ) ( ) ( > ′ ′ b f a f ) , ( b a ∈ ξ ) ( = ξ f ) ( , ) ( > ′ > ′ b f a f ) ( ) ( lim > − − + → a x a f x f a x > δ ) , ( δ + ∈ ∀ a a x ) ( ) ( = > a f x f ) , ( 1 δ + ∈ a a x ) ( ) ( 1 = > a f x f ) , ( 2 b b x δ − ∈ ) ( ) ( 2 = < b f x f ) , ( ) , ( 2 1 b a x x ⊂ ∈ ∃ ξ ) ( = ξ f ) ( x f ] , [ b a ) , ( b a ) , ( b a ∈ ∃ ξ a b a f b f f − − = ′ ) ( ) ( ) ( ξ 2 www.etsinghua.org 010-62701055/82378805 B 503 ) )( ( ) ( ) ( a b f a f b f − ′ = − ξ ) ))( ( ( a b a b a f − − + = θ ) 1 ( < < θ ) )( ( ) ( ) ( x x f x f x f − ′ + = ξ h f x f h x f ) ( ) ( ) ( ξ ′ + = + ) , ( b a x ∈ ∀ ) ( = ′ x f c x f = ) ( c ) , ( b a x ∈ ∀ ) ( ) ( x g x f ′ = ′ ) , ( b a c x g x f + = ) ( ) ( ) ( x f y = ) ( x g y = ) , ( ), , ( b a x y x ∈ ) ( ) ( x g x f = ) ( x f ′ ] , [ b a ] , [ b a 2 1 , x x > L 1 2 1 2 ) ( ) ( x x L x f x f − ≤ − ) , ( b a x ∈ ∀ ) ( ≥ ′ x f ) ( x f y = ) , ( b a ) ( > ′ x f ) ( x f y = ) ( ≤ ′ x f ) ( < ′ x f ) ( x f y = ) ( < ′ x f ) ( x f y = ) ( x f y = 1 x 1 x ) ( x f ) ( x f ] , [ b a ) ( x f y = 3 www.etsinghua.org 010-62701055/82378805 B 503 2007 1 2 ) ( x f ) , ( +∞ ) ( > ′ ′ x f ) ( n f u n = L , 2 , 1 = n A { B 2 1 u u > } n u 2 1 u u > { } n u C D 2 1 u u < { } n u 2 1 u u < { } n u D 1 2 D 2 1 u u < , 1 2 > > − c u u c ) 2 , 1 ( 1 ∈ ξ ) ( 1 2 ) 1 ( ) 2 ( 1 2 1 1 2 > > ′ = − − = − − c f f f u u ξ ) , ( 1 +∞ ∈ ξ x ) ( > ′ ′ x f ) ( x f ′ ) ( ) ( 1 > > ′ > ′ c f x f ξ ) , ( 1 2 x ξ ξ ∈ ) )( ( ) ( ) ( 1 2 1 ξ ξ ξ − ′ + = x f f x f ) ( 2 > ′ ξ f +∞ = ∞ →= ) ( lim x f x { } n u Lagrange 36 5-3 4-42 4-43 2 28 3 = ) ( x f 2 x , (0 ) ( x f , ) +∞ ) ( > ′ ′ x f 2 1 u u < (C); = 2 { } { } n u n = ) ( x f 1 x , ) ( x f (0, ) +∞ 1 ( ) 0, 2 f x u ′′ > > u 1 { } { } n u n = (B); ( ) ln f x x = − ) ( x f (0, ) +∞ 1 ( ) 0, 2 f x u ′′ > > u n { } { ln } n u = − (A)....
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2009è€ƒç ”æ•°å­¦å¼ºåŒ–ç

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