1、2014 c IpmK (B ) Y W K 0 8 = OKJ o IO. K g Yg1 . AO 5 = YXJ)S ) p ) g n! ( S gIO.1 !W K 1!ef(x) d g : (0;0);(1;1) (2;3) Kf 1(2) = 32.) y = 2 : 32;2 f 32 = 2l f 1(2) = 32.2!3Xe NABCD A0B0C0D0 A0 BD C0 u arccos 13 (n L).) AC BD : O. w,AC?BD nR nA0O C0O R uBD A0OC0.b N c 1. A0C0 = p2;A0O = C0O =p62 . d
2、un cosA0OC0 = 13 A0 BD C0 u arccos 13.AOI 5 n L X 2 arctanp22 .3!u8R ?f8U 3R fU(x) =(1 x2U0 x62U :XJA;B8R f8KfA(x) +fB(x) 1 7 A;Bp 8.) u? x 2 R;fA(x) + fB(x) = 1 fA(x);fB(x) k 1=x2AB. AB = R. , fA(x);fB(x) =k 1= AB = ?. l A;Bp 8.p 8 kN XAB = R;AB = ?.14!XJn / ABC n S A;B;C cotA;cotB;cotC g KB 3 .) P
3、x = cotA;y = cotB;z = cotC = 2y = x+z. dun S u x;y;z k u u“y 0. , A+B = C % xy 1x+y = z;=xy +yz +zx = 1. z x2 2xy + (1 2y2) = 0. ux k O“ = 12y2 4 0. cotB = y p33 =B 63 . A = B = C =3 B .5! fang v a1 =p22 + 1;a2 =p2 + 1;an+1 + an 1 = nan an 1 + 2(n 2)K “an = np2 + 1 (n 1).) O A “an = np2 + 1 e58By (J
4、. w,n = 1;2 ( . bn6k “oak+1 = ak 1 + kak ak 1+ 2 = k 1p2 + 1+ k1p2+ 2 = k + 1p2 + 1:=n = k + 1 “ . y ( .6!F1;F2 x2a2 + y2b2 = 1 (a b 0) :P :. XJ PF1F2 1tanPF1F2 = 12;tanPF2F1 = 2. Ka =p152 .) b F1 = F1( c;0);F2 = F2(c;0);(c 0) P = P(x0;y0). F1;P k1 = tanPF1F2 = 12 F2;P k2 = tanPF2F1 = 2. d 81).fi a1
5、 = 1;a2 = 5 an “.) kS1 = 1;S2 = 6;S3 = 6 +a3 S1 +S2 +S3 = 22 % a3 = 9;S3 = 15. a4 = 13.dSn 4 “ kSn+1 +Sn+2 +Sn+3 = 6n2 + 21n+ 22an+1 +an+2 +an+3 = Sn+3 Sn = 12n+ 15=an +an+1 +an+2 = 12n+ 3;n 2:d“ an+1 +an+2 +an+3 = 12n+ 15 an+3 an = 12. a3k 1;a3k a3k+1 O 12 Oa2 = 5;a3 = 9 a4 = 13.5 a1;a2;a3;a4 4 . a
6、n 4 “ an = 4n 3 (n 1).) a3 = 9;a4 = 13;: an “an = 4n 3 e5B8By “w,n = 1;2 “bn 6 k;(k 2) “o n 6 k kSn = 2n(n+ 1) 3n = 2n2 n. 4 “ kak+1 = Sk+1 Sk = (Sk+1 +Sk +Sk 1) 2Sk Sk 1= 6(k 1)2 + 9(k 1) + 7 4k2 + 2k 2(k 1)2 +k 1= 4k + 1 = 4(k + 1) 3 y“310! x1;x2;x3 “ x3 10x+ 11 = 0 n .a) fi x1;x2;x3 3m ( 5;5) n b
7、) y arctanx1 + arctanx2 + arctanx3 = 4 .( IO p a) S J 5 b) 15 ) a) P(x) = x3 10x + 11 kn . du P( 5) = 64;P( 4) =13;P( 3) = 14;P( 2) = 23;P( 1) = 20;P(0) = 11;P(1) = 2;P(2) = 1;P(3) = 8;: w 3n m ( 4; 3);(1;2) (2;3) :P(x) UC n O3n mS 4;1;2 B v n Cq .5 u 3m ( 4; 3) XJ 3 (. vk( o .b) bx1 1arctanx2;arcta
8、nx3 2 4; 2 . l arctanx1 + arctanx2 4 arctanx3 3m 4; 4 =I y tan (arctanx1 + arctanx2) = tan4 arctanx3v . | “ “S du x1+x21 x1x2 = 1 x31+x3 Jw 1 “ q du 3Xi=1xi +Xi6=jxixj x1x2x3 = 1:d X X k3Xi=1xi = 0;Xi6=jxixj = 10;x1x2x3 = 11: “. y.11!Xe : x24 + y2 = 1;A( 2;0);B(0; 1) : 1 : x =2;2 : y = 1. P(x0;y0) (
9、x0 0;y0 0) :“3 L:P C;D;EO 1 22 31 3 :“yn AD;BE CP :“) 3 x0x4 +y0y = 1C;D;En: IO ( 2; 1);4(y0 + 1)x0 ; 1;2;x0 + 22y0:4 5AD x0(x+ 2)2(2 +x0 + 2y0) +y = 0;BE x2 +2y0(y + 1)2 +x0 + 2y0 = 0:e5k Xe S : x0(x+ 2)2(2 +x0 + 2y0)+y + x2 +2y0(y + 1)2 +x0 + 2y0= 0:w,S LAD BE :. XJ LC C( 2; 1) ) = 1. S 1 LAD BE :
10、 C . yP 3 S 1 =x0(x0 + 2)2(2 +x0 + 2y0) +y0 x02 +2y0(y0 + 1)2 +x0 + 2y0= 0: yXe “ x0(x0 + 2) 4y0(y0 + 1)2(2 +x0 + 2y0) =x02 y0: 2 +x0 + 2y0 x202 +x0 2y20 2y0 =x02 y0(2 +x0 + 2y0) = x0 2y0 + x202 2y20:CP (LAD BE :. I ( ., K 5 .) |c AD BE O X :Q I(J 8y0(y0 + 1)(2 +x0 + 2y0)2 2x0y0; x0(x0 + 2)(2 +x0 +
11、2y0)2 2x0y0 CQ kCQ =1 x0(x0 + 2)(2 +x0 + 2y0)2 2x0y02 8y0(y0 + 1)(2 +x0 + 2y0)2 2x0y0= 2 + 2y20 +x0 + 4y0 +x0y04 +x20 + 4x0 + 4y0 + 2x0y0= (2 +x0 + 2y0)(y0 + 1)(2 +x0 + 2y0)(x0 + 2)= y0 + 1x0 + 2; u CP . Q3CP I ( .) n | Ceva n. duEAAC CBBD DPPE =x0 + 22y0 2x04(y0 + 1) y0 + 1x0 + 22y0 y0= x0(x0 + 2)2
12、(x0 + 2) 4y20;P(x0;y0) 3 x204 +y20 = 1 x0(x0 + 2)2(x0 + 2) 4y20 =x0(x0 + 2)2(x0 + 2) +x20 4 = 1:5=EAAC CBBD DPPE = 1:Ceva nAD;BE CP n :.1 !Xe H n R :A;B;Cn:K, n :.a) yH n / ABC R%b) yn / ABC uR.( IO a) b) 20 ) O1;O2;O3 On %Xe o/AO2HO1 O2BO3H uR !/. 5AO1 kO2HkBO3 . o/ABO3O1 1o/=ABkO1O3 .a) duCH O1O3
13、!/CO1HO3 pR CH AB R . nAH;BH OR u ABC BC;AC. y H ABCR%.b) du AB = O1O3 n BC;AC O u O1O2 O2O3. n / ABC O3O1O2 . H n % l R O3O1O2 R. yABC uR.!3 IXf(x) =pax+ 4;(a6= 0) y = f 1(x) Tkn :a y ( .6) f(x) = pax+ 4 f 1(x) = 1a(x2 4);x 0 : I (u;v).Jw : I K .5 u;v v | 80o 31 u + v + a 0. u = v u2 = av + 4 ) : (
14、, )K ). K8 b kn : Uu). k a 0 a p 3a2 + 16 0. =jaj 2. q a 2a;b “ a+b . b akx bky = a bk )x;y 0 2p3 n /. 3n / ABC S . ? 11:a) y 3 : m l u u 1b) y 3 : m l u 1.( IO a) b) O 20 30 ) a) Xe ABC 16 p32 n /um 8 n / n n / 5 w ABC m 10 8/CX“7Jw p 10 8/ 1. w 10 T“. un /ABC S . ? 11 : T n k 8/ :. 38/? : m l m l L 1. By I ( .5 T E . XJe 10 12 CXABC ( .b) y . y3 11 : 3 : m l u 1. 5 3 1 8/m T 1 : l ”:. , E 8/T“3 ”:?kE . L ”:u A 8/5UE T“z T“ 8/ l 1 ”:. ,3y3 / =I %”: UE v . 8 3z 8/T“ K ”: z T“ 2 8/ l 1 ”:. e U UE % Ll 8/ KT”:. Jw UE CX 5 n / ABC z T“ 2 8/ l 1 ”:. T n 8y ? 11 : 3 : m l u 1. T“ E .9
