? tc?s   5 ?s¥à Q? VHq 1. ¨?l9 ?/ ?s ò ()ax b dx+ ∫ 0 1 ; ó adx x 0 1 ∫ (a ). > 0 3  1 |?s 1 121 0 < ? <<<< n n nn " # ),,2,1( ni n i i "==ξ 5 n x i 1 =? ? ^ )( 2 ) 1 1( 2 1 )( 1 ∞→+→++=+ ∑ = nb a b n a n b n i a n i ' b a dxbax +=+ ∫ 2 )( 1 0 b  2 | ? s  1 121 0 < ? <<<< n n nn "  # ),,2,1( ni n i i "==ξ  5 n x i 1 =?  ? ^ )1( )1(1 1 1 1 n nn i n i an aa n a ? ? = ∑ = by1 )(ln 1 1 1 ∞→→ ? na n a n  )(1 1 ∞→→ na n  ?[ a a an aa n a n nn i n i ln 1 )1( )1(1 1 1 1 ? → ? ? = ∑ =  ' a a dxa x ln 1 1 0 ? = ∫ b ? £ ü ? [, ¥ ?i?s? ?i]ab ∈ i ξ [,xx ii?1 ] K ?i5 A ^ [, ¥μ?f ?b ∑ = → ? n i ii xf 1 0 )(lim ξ λ fx() ]ab £ ¨Q£Eb ! ∑ = → ? n i ii xf 1 0 )(lim ξ λ I= 5 | 0,1 >?= δε   ?i¥?s D ?i P 1 [, ii ] i x xξ ? ∈ o1 δλ <?= ≤≤ )(max 1 i ni x  üμ 1)( 1 +<? ∑ = Ixf n i ii ξ b |? ?sa nD (1,2, i )x?=" n ] 9ü ?? ?T  [, í ?5A?il uW fx() ]ab 1 [, ii x x ?  fx() 1 [, ii ]x x ? í?b |? 203 111 ,, , ,, ii n ξ ξξ ξ ?+ ""A V |? i ξ  P 1)( 1 +<? ∑ = Ixf n i ii ξ ?? ?V 7á 3 ± ?[ A ^ [, ¥μ?f ?b fx() ]ab à £ ü Darboux? ?¥a??s ?iμ?f ? ?μ fx() lim ( ) λ→ = 0 SP lb £ 0>?ε y1 ^l S¥  ?? ?[ S∈′? )(PS  P¤ 2 )(0 ε <′?≤ PSl b !?s bxxxxaP p =′<<′<′<′=′ " 210 :  ^ ¥ a/ ?? | mM , fx() ? ? ? ? ? ? ? ? ?? ′?′?′?= ))(1(2 ,,,,min 21 mMp xxx p ε δ "   ?iB? ?@ δλ <?= ≤≤ )(max 1 i ni x ¥?s bxxxxaP n =<<<<= " 210 :  :D M?¥l?1 )(PS C| PP ,′ ¥s??B F??¥?s P′′5?? ? 7.1.1 0)()( ≤′′?′ PSPS b / ? ?9 )()( PSPS ?′′   1 ? ? àμ),( 1 ii xx ? P′¥s?5 )(),( PSPS ′′ ?¥M?[M]  ? ì¥μ1 ,  2 ? ?cμ),( 1 ii xx ? P′¥s??? ??s¥ ?×? ? [?"¥ uWàoμ 1?p ?b? δ¥ |E V? pjnixx ji ,,2,1,,,2,1, "" ==′?≤≤? δ  ?[ ?oμB??? ?¥s?),( 1 ii xx ? j x′? H )(),( PSPS ′′ ?¥M ?[¥μ1 )()]()([ 11 ?? ??′?′′+?′′ iiijiiiji xxmxxmxxm ))(( 1? ??≤ ii xxmM δ)( mM ?<  204 V7 2 ))(1()()(0 ε δ ≤??<?′′≤ mMpPSPS b 8?  ?¥2 ?üμ )]()([)]()([)]([)(0 PSPSPSPSPSlPSl ?′′+′′?′+′?=?≤ ε εε =++< 2 0 2  ' lPS = → )(lim 0λ b á £ ü? ? 7.1.3b £ A1? ^A ?¥/ ?£ s?b ! 0>?ε iB??s P′ P¤M?¥?? ? @ 3 1 ε ω <′?′ ∑ = p i ii x  ' 3 )()( ε <′?′ PSPS b | ? ? ? ? ? ? ? ? ?? ′?′?′?= ))(1(3 ,,,,min 21 mMp xxx p ε δ "   ?iB ? ?@ δλ <?= ≤≤ )(max 1 i ni x ¥?s bxxxxaP n =<<<<= " 210 :  C| ¥s??B F??¥?sPP ,′ P′′ 5? Darboux? ?¥£ ü V? V¤ )]()([)]()([)]()([ )]()([)]()([)()(0 PSPSPSPSPSPS PSPSPSPSPSPS ?′′+′′?′+′?′ +′?′′+′′?=?≤ ε εεε =++++< 3 0 3 0 3  ?? ? 7.1.1 V?   Vb )(xf ],[ ba ? ) ?/ f ? [0,1] ¥ V? ò fx() ? ? ? = ≠? = ;0,0 ,0],[ 11 x x xx ó fx() ? ? ?? = ;,1 ,,1 1í ? ? 1μ ? ? x x ? fx() ? ? ? = ;, ,,0 1í ? ? 1μ ? ? xx x ? fx() ? ? ? = ≠ = .0,0 ,0),sgn(sin x x x π 205 3   1 0(  O  [0,1] ¥? ???1)fx≤<1 )(xf 11 1 ,, ,, 23 x n = ""D 0x= b 0>?ε  | ? ε 2 >m   uW)(xf ]1, 1 [ m oμμK?? ??? ?[ )(xf ]1, 1 [ m  V'i ]1, 1 [ m ¥B??s  P¤ P 2 1 ε ω <? ∑ = n i ii x | ¥s?? 0?B T1 [0,1]¥?s 5 P 'P ε εε ωωω =+<′?′+?=′?′ ∑∑ = + = 22 11 1 1 1 xxx n i ii n i ii  ?? ? 7.1.3  [0,1]  Vb )(xf  2y1 [0,1]¥ ?i?s 9μ P 2= i ω  ?[ ? 2 1 =? ∑ = n i ii xω ? ? 7.1.2 V?  [0,1] ? Vb )(xf  3y1 [0,1]¥ ?i?s P  ¥??1 ? ^ )(xf ],[ 1 ii xx ? i x ∑∑∑∑ = ? = ? ? = ? = ?=? + ≥?=? n i ii n i ii ii n i iii n i ii xxxx xx xxxx 1 2 1 2 1 1 1 1 1 1 )( 2 1 )( 2 )(ω 2 1 )( 2 1 2 0 2 =?= xx n  ?[  [0,1] ? Vb )(xf  4  O  [0,1] ¥? ???11()fx?≤ ≤1 )(xf 11 1 1, , , , , 23 x n = ""D 0x= b 0ε?> |? ε 4 >m 5 )(xf ]1, 1 [ m oμμK?? ??? ?[ )(xf ]1, 1 [ m  V'i ]1, 1 [ m ¥?s  P¤P 2 1 ε ω <? ∑ = n i ii x b | ¥s?D 0?B T1 [0,1]¥?s 5 P 'P ε εε ωωω =+<′?′+?=′?′ ∑∑ = + = 22 11 1 1 1 xxx n i ii n i ii  ?[  [0,1]  Vb )(xf 6. !   V O [,  ?@  m1è ?  fx() [, ]ab ]ab 0|)(| >≥ mxf 206 £ ü )( 1 xf  [, 9 Vb ]ab £ ? | ¥B??s[, ]ab bxxxxa nn =<<<<= ?110 " 5 )( 1 ))()((sup 1 )( 1 )( 1 sup) 1 ( 2 , 2 , 11 f m xfxf mxfxff i xxxxxxxx i iiii ωω =′′?′≤ ? ? ? ? ? ? ? ? ′′ ? ′ = ≤′′′≤≤′′′≤ ??  ??   Vfx() [, ]ab 0,0 >?>? δε ? δλ <?= ≤≤ )(max 1 i ni x H V7 εω 2 1 )( mxf n i ii <? ∑ = εω <? ∑ = n i ii x f 1 ) 1 (  ?[ )( 1 xf  [,  Vb ]ab 7. μ?f ?  ¥? ???1 {} O i£ ü fx() [, ]ab x nn= ∞ 1 lim n n x →∞ fx()  Vb [, ]ab £ ?^ !  Olim n n x →∞ c= ),( bac∈ i ! Mxf ≤)( b 0>?ε  | ? ? ? ? ? ? ??= cbac M ,, 12 min ε δ 5 0>?N ? HNn > δ<?cx n b ?? fx() ],[ δ?ca ? ],[ bc δ+ oμμK?? ??? ?[ fx()  ],[ δ?ca ? ],[ bc δ+ ? V'i ],[ δ?ca ¥B??s )1( P ? ],[ bc δ+ ¥B??s )2( P  P¤ 3 , 3 )2()2()1()1( ε ω ε ω <?<? ∑∑ i ii i ii xx b| )1( P a )2( P ¥s??iB F? [, ¥B??s 5 ]ab P 1 n ii i xω = ?≤ ∑ ε εεε δωω =++<+?+? ∑∑ 333 4 )2()2()1()1( Mxx i ii i ii  ?[  [,  Vb fx() ]ab ca=  ¥ f ? V ? ?£ üb cb= 8 ! ^ uW ¥μ?f ?b£ ü   V¥ s )(xf ],[ ba )(xf ],[ ba A1Hq ^ ?ió?¥ 0>ε D 0>σ  i?s P P¤?? εω ≥ i ¥ *tl uW ¥é-?],[ 1 ii xx ? ∑ ≥ <? εω σ i i x  '??? ? ?il¥ *tl 207 uW¥é-? V[ ?il b £  s? : ! Mxf ≤)( b 0>=? σε , i?s , P¤??P εω ≥ i ¥ *tl uW¥é-? ∑ ≥ <? εω i i x ε , ? ^ εωωω εωεω ]2)[( 1 Mabxxx ii iiii n i ii +?<?+?=? ∑∑∑ ≥<=  '   Vb )(xf ],[ ba A1? ¨Q£E ?Ti 0 0 >ε D 0 0 >σ   ?i?s P ?? 0 εω ≥ i ¥l uW¥é-??l? 0 σ , ? ^ 000 1 000 εσεωωω εωεωεω ≥?≥?+?=? ∑∑∑∑ ≥≥<= iii iiiii n i ii xxxx  5? ()0max 1 →?= ≤≤ i ni xλ H  ∑ ? t? , D   V ± b = ? n i ii x 1 ω )(xf ],[ ba 9. !   Vfx() [, ]ab Afx B≤ ≤() ,  [,  ??£ üˉ? )(ug ]AB f ?  [,  Vb gfx(() ]ab £ ??  ?? , ?[ V !)(ug ],[ BA Mug ≤)(  O Bá ?? , ? ^ )(ug 0>?ε , 0>?δ , , o1],[",' BAuu ∈? δ<? "' uu , ü? ? )(2 )"()'( ab ugug ? <? ε b ??  V , ?5 8,   ?)(xf ],[ ba 0>ε D 0>δ , i?s P , P¤?? δω ≥)( f i ¥l uW¥é-?l? M4 ε , ? ^ ∑∑∑ ≥<= ?+?=? δωδω ωωω )()(1 )()()( f ii f ii n i ii ii xfgxfgxfg DDD ε εεε δωδω =?+? ? <?+? ? < ∑∑ ≥< M Mab ab xMx ab f i f i ii 4 2)( )(2 2 )(2 )()(  'ˉ?f ?  [,  Vb gfx(() ]ab 208