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2003()(6,36)1.a,x.M:x{-a,a},N:x2=a.MN().(A)(B)(C)(D)2.[a]a,y=x-x-|sinx|().(A)-22(B)12(C)1(D)3.f(x),f(x+5)=-f(x),x(5,10),f(x)=1x.f(2003)().(A)-18(B)15(C)13(D)-134.9x-23x-30x().(A)-1(B)0(C)1(D)35.ABC,AB=5,AC3,BC7.CAB().(A)2(B)23(C)34(D)566.||x2-4x-5|-6|=ax6,a().(A)-6a0(B)0a3(C)3a6(D)6a9(8,64)1.ABCD,MBC,NCD.sinMAN.2.min{a,b,c}abc.xy,M=minx,1y,y+1x.3.f(x)=2+x1+x.f(1)+f(2)++f(1000)=m,f12+f13++f11000=n.m+n.4.x1x2x+4+9-3x=5,,x21+x22.5.ABC,ABC=36,ACB=42,BCD,BDABC.DAC=.6.{an},a1=1,an+1=4an+4an+1,n=1,2,..7.n,f(n)=sinn2.f(1991)+f(1992)++f(2003)=.8.,,q.(8,40)1.xy,xy+x+y=71,x2y+xy2=880.x2+y2=.2.1,AB,S1,SAC,D,SBE,F.CE=a,DF=b,ABECABFD.AB=.3.f(x)=3x-1,x,x2,x.x1=12,xn+1=f(xn),nN,{x|x=xn,nN}.4.{bn}{an},b3-b1=9,b5-b3=36,b1=a1,b2=a3.6G6,12A12,G6+A12=.5.M={-2,0,1},N={1,2,3,4,5}.f:MN,xM,x+f(x)+xf(x)..(15)abc,:a3a2+ab+b2+b3b2+bc+c2+c3c2+ca+a2a+b+c3.22©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(15)2,PAB=1,223().AP=x,BP=y,k=3x+2y.(15)RrP,Pd.:1R+1r=2d.(15)na1,a2,,an.t1a1+t2a2++tnan(ti1-1,i=1,2,,n),n2+n+22,,.1.B.a,x=-a,x{-a,a},M.(-a)2=a-a,N.,MN.N,x2=a,a.a0,a.,x=a{-a,a},M.,MN.,MN.2.D.0x-x1,0|sinx|1,y=x-x-|sinx|1-0=1,y=x-x-|sinx|1.1.y,x(0,].x(0,],x(0,),x=0,sinx0,y=x-sinx1-sinx1.33,xx1,y0,x(x1,),xsinx,x,sinx,y=x-sinx;x=,y=0.,y.3.A.f(x+10)=-f(x+5)=f(x),,f(2003)=f(20010+3)=f(3)=-f(8)=-18.4.C.3x=t,t2-2t-30.t(-,-1][3,+).t,,3x=t3.x1.,9x-23x-301.5.B.cosCAB=AC2+52-BC225AC32+25-7210AC=-1510AC-15103=-12.(0,),,CAB23.6.C.y=||x2-4x-5|-6|,y=a,a3a6.1.35.44,2,MN,SABCD=4,SABM=SADN=1,SCMN=015.,SAMN=4-1-1-015=115.AM=AN=5,SAMN=12AMANsinMAN,sinMAN=211555=35.2.2.1yM,xM,y+1xM,y1M,1x1M,My+1x2M.,M22,M2.x=2,y=12,1y=2,y+1x=12+12=2.,M=2,M2.3.299815x-1.f(x)+f1x=2+x1+x+2+1x1+1x=3,f(1)=32,3220043©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=3999+32=299815.4.14116.x+49-3x=x+6,9x+36-3x2-12x=x2+12x+36,4x2+15x=0,x(4x+15)=0.x1=0,x2=-154..,x21+x22=0+22516=14116.5.54.OABC,BAC=5102.,OABC.OABCD1.D1D.5,AOB=84,OAB=48,BD1O=36+48=84.,BD1=BO,D1D.,DAC=102-48=54.6.22n-2n+1+1.an+1=2an+1,,an+1+1=2(an+1).,{an+1+1}22.an+1=2n,an=2n-1.,an=22n-2n+1+1.7.-1.f(1991)=-1,f(1992)=0,f(1993)=1,f(1994)=0,,f(2003)=-1.,f(1991)+f(1992)++f(2003)=-1.8.5-12q5+12.a,aq,aq2,a0,q1.a+aqaq2,q2-q-10.1-52q1+52.q1q1q1+52.a,aq,aq2,a0,0q1.aq2+aqa,q2+q-10.5-12q1.,5-12q5+12.1.146.a=x+y,b=xy,xy+x+y=a+b=71,x2y+xy2=xy(x+y)=ab=880.,abt2-71t+880=0.a=x+y,b=xy1655.x+y=55,xy=16,.,x+y=16,xy=55.,x2+y2=(x+y)2-2xy=146.2.a2+b22.SCE=SBA=SDF.,SCESBASDF.AB=x,SSCE=S0,SABEC=SABFD=S,S0+SS0=x2a2,S0+2SS0=b2a2.SS0=x2-a2a2,2SS0=b2-a2a2,x2-a2a2=b2-a22a2.x=a2+b22.3.7.x1=12x2=6,x3=3,x4=8,x5=4,x6=2,x7=1,x8=2,x9=1,,2,1,2,1,.,xn7,{x|x=xn,nN}7.4.324.q(q0),b1q2-b1=9,b1q4-b1q2=36,b1q2-b1=9,q2(b1q2-b1)=36.q2=4.q=2q=-2.q0,q=2.b1=3.,G6=b1(1-q6)1-q=3(1-64)1-2=189.d{an},a1=3,a1+2d=6.d=32.,a12=a1+11d=392.,A12=(a1+a12)122=3+3926=135.42©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=189+135=324.5.45.f:MNM={-2,0,1},f(x)N={1,2,3,4,5}.xM,x+f(x)+xf(x).x+f(x)+xf(x)=x+xf(x)+1+f(x)-1=(x+1)[1+f(x)]-1.x=1,x+1,f(x)N,x+f(x)+xf(x).,f(x)5.x=-2,x+1,x+f(x)+xf(x),1+f(x),f(x).,f(x)3.,x=0,f(x)3.,335=45.a2+ab+b23ab,,a3a2+ab+b2=a3+a2b+ab2-(a2b+ab2)a2+ab+b2=a-ab(a+b)a2+ab+b2a-a+b3.,b3b2+bc+c2b-b+c3,c3c2+ca+a2c-c+a3.++,a3a2+ab+b2+b3b2+bc+c2+c3c2+ca+a2(a+b+c)-2(a+b+c)3=a+b+c3.APB,x2+y2-2xycos23=1,x2+y2+xy=1.k=3x+2yy=k-3x2.7x2-4kx+k2-4=0.x,.,=(4k)2-47(k2-4)0.k2283.k2213.k=3x+2y=x+2(x+y)x+22,,2k2213.x=42121,k=2213;PA,k=2.,2213,2.66,ROrO1P,AB,PCABC.OPO1P,OPO1.BO1O1D,BDO1.APPD.OABD,,AOP=PO1D.AOPPO1D,OPA=O1PD.,APD.PCDB,,APAD=PCDB=d2r.AOPDO1P,APDP=OPO1P=Rr]APAP+DP=RR+r]APAD=RR+r.,RR+r=d2r]R+rRr=2d.1R+1r=2d.a1a2an,a=-a1-a2--ant1a1+t2a2++tnan,a+2a1=a1-a2--ant1a1+t2a2++tnan.,a+2a1+2a2t1a1+t2a2++tnan.,a1a+2a1a+2a2a+2anna+2an+2a1a+2an+2an-1n-1a+2an+2an-1+2a1a+2an+2an-1+2an-2n-2a+2an++2a3+2a1a+2an++2a3+2a22a+2an+2an-1++2a2+2a11=a+2(a1+a2++an)=a1+a2++an.t1a1+t2a2++tnan(ti1-1,i=1,2,,n),1+n+(n-1)+(n-2)++2+1=1+n(n+1)2=n2+n+22.,a,n2+n+22;a,n2+n+22.()5220043©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.