24 - +P N * N 912401 6 6 7 0 6 6 7 6 7 6 6 6 X X X 6 6 X 6...

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Unformatted text preview: +P N * N 912401 6 6 7 0 6 6 7 6 7 6 6 6 X X X 6 6 X 6 X 6 6 6 X 6 6 6 6 0 X X X X 912402 912403 1 X X 7 1 X 7 7 X 1 7 X X X X 7 7 6 7 6 7 7 X X 7 7 7 7 2 6 6 6 6 912404 X X x 0 0 X X 7 X X 7 7 X X X X X X X X X X X X X X X X X X X X X 912405 X X X 5 X X X 4 5 X X X X X X X X X X X X X X X X X X X X X X X X 7 6 7 12 7 6 14 24 12 7 27 13 7 7 7 13 13 6 13 6 13 13 6 7 13 13 13 13 2 6 6 6 6 X9 X X X X X X X X X 7 X 7 7 7 X X X X X X X X 7 X X X X X X X X X X X X X X X X 6 6 6 X X X X * ª ¶ Å H Ý 6 X 6 6 X 7 6 * ª ¶ Å H Ý * ª ¶ Å H Ý 6 6 6 6 6 * ª ¶ Å H Ý * ª ¶ Å H Ý * ª ¶ Å H Ý 7 6 6 6 6 6 X 6 6 6 0 0 6 X X X X X X X X X X 7 7 7 7 X X 6 7 7 7 7 7 7 X 7 X 7 X 7 X X 4 X X X X X X X 2 6 6 2 6 6 6 7 7 7 X X X X 7 0 7 2 X 1 0 7 3 6 5 2 2 X 7 X 2 2 X 0 3 X X 0 X X X X X X X X X X X X X X X 7 X X X 7 7 X 7 7 7 7 X 7 7 7 7 7 7 0 5 X X X X X X X X X X X X X X X X X X X 4 X X X X X 0 0 X X X X 0 X 3 X X X X X X X X X X 2 6 6 2 6 6 6 13 13 13 7 7 7 7 24 0 19 15 14 22 13 27 23 19 25 8 23 13 30 13 15 19 0 11 9 6 0 0 6 6 6 6 7 6 6 0 0 6 X 0 6 0 6 X 6 7 6 6 6 X X X 0 X 6 0 X X X X 6 0 0 X X 6 X X X X X 3 3 3 0 X X 0 X X X 0 X X X 0 7 7 X X X X X X 0 X X X X X X X X X X X X 7 X 0 5 7 6 X 3 X X X 1 7 1 0 0 2 6 7 7 X X X 1 X X 1 0.5 2 0 1 X X 1 X X X 2 X 7 X X 7 7 7 7 X X X X 7 7 7 X X X X 7 0 7 7 7 X 7 X 7 X X X X X X X 7 7 X 7 7 X X X 4 4 0 0 X X X X 4 X 4 X 1 0 0 X 5 X X X X X X 0 X X X X X X X X X X X X 20 6 6 26 27 22 7 3 6 0 0 18 14 18 0 7 9 12 27 25 7 7 7 1 7 6 8 0.5 2 0 1 6 0 1 7 7 6 9 7 0 X X X X 6 X X X X X X X X 6 6 X 6 X 6 X X 6 X X 6 X X X 6 X X X 6 X 0 X 0 6 X X X X X X X X X X X X X X X X X X X X X X 7 X X X X X X X X X X X X X 0 X X X 1 X X X 1 X X X 0 X X X X X X X X 7 X X X 1 X X X 2 2 2 X 2 1 X X 1 X 0 X X 7 7 7 7 7 7 7 7 7 7 6 7 7 7 7 7 7 7 7 7 7 0 X 7 7 X X X X X X X 7 7 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 7 8 7 7 7 14 7 7 7 7 6 7 7 7 13 13 7 13 14 13 7 0 14 7 7 6 2 2 2 6 2 1 7 13 1 0 0 0 6 X 6 6 X X 0 X 6 0 6 0 ä ä ä 93 7 4.91 X X X X X X 0 X X X 7 34 22 5.09 0 X X 2 7 2 0 X 0 0 1 94 27 3.64 X 7 7 X X X X 7 5 0 7 71 62 6.34 X X X X X X X X X 7 X 20 1 2.5 0 13 13 2 7 2 0 13 5 13 15 312 119 22.48 h Ç ¶ ä p˜ P + N @ * ª ¶ Ç ! @ª xÇ ¶ ( )xÇ @ª *¶ à˜ P + N @ K * ª ¶ Ç ! 912401 9 (20029 )2 9 20022002 x *ª¶Ç@ (9 n9 =n ×(n─1) ×(n─2) ×… ×2 ×1 ,¶ Ç n x @ ¶ Ç @ èª * N k= 9 k=xxx…x ɘ n(2003-n)9 1≦n≦2002∴ n 9 ∴ -n2+2003n = -(n2-2003n) =-(n-)2+()2 9 ∵1≦n≦2002 ∴n(2003-n)è ª ¶ Ç@ 20029 1004003 ∴≦1 k<1 ∴(2002∴ )2>200220029 ) N 20022002=(20021001)2 (20029 )2=[2002x(2002-1)x(2002-2)x…x1]2 ={[2002x1]x[(2002-1)x2]x[(2002-2)x3]x…x[(2002-1000)x1001]}2 9 2002b E ª· ] 2002 b E *ª · ] 1001 m=09 19 22… 1000 4qÀ (2002-m)x(m+1)ª Eb] · ∵m=0∴ 1 2 … ∴(2001-m)m≧0 ∴(2002-m)x(m+1)≧2002 ∴2002∴ >20021001 ∴(2002∴ )2>20022002 ªb ( · ªb ( ·* +. PN D 9 (2002-m)x(m+1)=2002m-m2+2002-m=2002+(2001-m)m 1000 ªb ( ·* 93ªE * ·] b 9 ·E ªb* ] 7PD + N 9 ·E ªb* ] 4.91 { 9 9 912402 { E º A p EP}º · 0 @ ‹ @ ‹ + B ]~ @ ƒ ∠ ACB m ˆ • NP. C + B․ A․ ∴ C․ ª{ · (1)· * ª{ + P [ AÕ á * B · P{ K ª B․ A․ L P․ Q․ ․ E C ․ D ․ (2) C1 A B CC * ª ¶ Ç 8 P C2 A B C * ª ¶ 8 Ç L ED x AB C Ç * ª ¶ 8 ∠ ACB=∠APB ∴ ADB=∠ AQB ∠ ∴ APB > ∠AQB ∠ ∴ ACB > ∠ADB∴ ∠ ª ¶ 8C Ç ∴ * ª ¶ 8C Ç ¨•§ @ E º Š + P 34 8Ç C¶ * ª 9 ¶ Ç C 8ª* 22 N + P D 9 9 5.09 ¨•§ Q 9 912403 9 2x2 ─11[x]+12=0 9 ([x]8 ª¶ ÇC *ª ·anÈ 1.9 ª ∵[x]È ·a n 2.9 9 x9 ª · a xÈ n ∴x-1<[x]≦x * ª ¶ Çx 8 C x=3.8→[x]=39 x=-0.4→[x]=-19 x=7→[x]=7) 2x2-11[x]+12=0 =>2x2+12=11[x] =>[x]= 9 x-1< 11x-11<2x2+12 =>2x2-11x+23>0 ∵(-11)2- 4•2•23<0 * ª ∴Èn ·a ÈÈ ≦ x ÈÈ ∵2x2+12=11x =>2x2-11x+12≦0 =>(2x-3)(x-4)≦0 ∴≦x≦4 (1) 1.5≦x<2 => [x]=1 ∴ 2x2-11[x]+12=0 =>2x2+1=0(9 ) (2) 2≦x<3 => [x]=2 ∴ 2x2-11[x]+12=0 =>2x2-10=0 => x2=5 =>x=±(9 ) ∴x=(9 ) (3) 3≦x<4 => [x]=3 2x2-11[x]+12=0 =>2x2-21=0 => x2= => x=±(9 ) ∴x=(9 ) (4) x=4 =>[x]=4 9 2x2-11[x]+12=0 =>2x2-32=0 => x2=16=> x=±4(9 ) ∴x=4 (9 ) 3. x x=9 4 1. 2x2-11[x]+12=0=> 2x2=11[x]-12 9 0<2x2=11[x]-12=>11[x]-12>0 =>[x]>9 [x]9 =>[x]≧2 2.9 x≧[x] ∴11x≧11[x]=2x2+12>2x2 =>>1 =><1 =>x<1 =>x<=5.5 9 [x]≦x =>[x]≦x<5.5 ∴ x 9 =>[x]≦5 3. 1 2 2≦[x]≦5 [x]=29 39 49 5 9 ([x]9 ) [x]=29 x=(-9 ) =39 x=(9 ) =49 x=4(9 ) =59 x=±(9 ) 9 x=9 4 ª¶Å E Þ ª¶Å E Þ [x]9 x9 9 *ª¶ Å E Þ =E [ 9 *9¶4Å E ªÞ 9 * ª ¶ ÅE Þ 27 + .D PN 9 * ª ¶ ÅE Þ 3.64 9 * ª ¶ ÅE Þ ¨ 9 9 912404 9 ABCD 9 * tª ¸· = =109∠ ABC=10009∠ CDA=13009 =9 9B à–ð ∵∠ABC=1000 ∴∠ABC4 ª ¸t· 1000 ∵AC 9 =26009 ∠CDA=1300 ª ∴4 ¸ ·D t 9 =109 * ª ¶E ÅÞ 9 A 10 1000 A 10 D 1300 ․100 B 0 10 C A D 1300 10 D 1300 ․100 B 0 10 C C B 10 * 1¶ .Å E ªÞ E 2.9 A9 D9 C ¨ E9 9 A9 D9 C9 EÅ E ª¶ Þ ∴∠AEC+∠ADC=18009 ∴∠AEC=500 3.9 ∠AEC¸ 9¸ ∠ ABC ¸ ¸¸¸¸ ∠ ABC=2∠AEC∴ =>B ¨ ∴∴ B 9 ∴=10=9 71 h·ª* Ú P+ . N D 9 · h Ú hª* 62 N.D P+ 9 · h Ú hª* 6.34 x 9 9 9 912405 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 Eºp ‹ïºEP‰`ö¶ª* x 1. 2. * 3.· h Ú h ª 4. ª·• x 1. x,y + P N x − 2 + x −3 + x − 4 + x −6 + x −7 + x −8 y − 0 + y −1 + y − 3 + y − 4 + y − 6 + y − 7 ª· x• * 2. 3. 3× 2 = 6 { x,y + P N y y − 0 + y −1 + y − 3 + y − 4 + y − 6 + y − 7 + y − 8 ª·(~ * ª·~ 4.( * ª·~ @ ( º‹ E @ 7 x=4 y=4 D (5,3),(6,3),(7,4) P Î ª6( ·~ x=4 5 6 y=3 4{ (6,4)( ª·~ 5 ïºEP‰`ö¶ª* º ‹E p x 7@‹ºEB E (1,8)˜ P N +p ! x −1 + x − 2 + x − 3 + x − 4 + x − 6 + x − 7 + x − 8 ª·~ *( 20·E ª~ * 1·E ª~ * 2.5+ À N˜K ª ·A P * ix ...
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This note was uploaded on 08/14/2010 for the course 數學 乙一 taught by Professor 鄭質明 during the Spring '07 term at Fudan University.

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