江蘇省海安中學2020屆高三階段測試三數(shù)學試卷5，，．UAAU(1(ii．zziz,,,aaa22+12，adSaaa123n122a+1，2a+1．3n25．．x2a2y2b2:ab1(0,0)10C線C．())()fxyxf634為．())(3)0，fxRfx2xfx．31，)3tan．ABCAABC5310Sa}nn3(1)()11nSnanN*aSnnnn220為．xyxy，yx．xABCDABCD，EF，BBCC111111EF//BCAAEFD．111，，0與，與ababcabcbc21，|2ac．b3f(x)m(x2m)(xm，()22gxx①，f(x)0或g(x)0；xR②x(,，f(x)g(x)0．則m．6ABC93AC(ABCB)18mAB,2)nAB)C；ABCc．2PABCDAB2，EF1，，，PC中BC//；EFABCDPAC．PACOM，OMONQA6知tanMON3OA6km，OMONkm，Q5ONQ．6kmPth為r3at(a182km/hABa36x2a2y2b2:ab1(0))E22、F．F122E、AB．EPEM(i)OPOMii)設Qkaa已知數(shù)列{}aa，(3,)．數(shù)列{}nnNn1aakkan1*bnnn123an2aan()．nNn2b*ann1b，b，b，b1234）求出數(shù)列b}na}kn4()()，．fxxaxaaR0()fxa0()(，)fxae2e2(,)，()1．xttafxaat5海安中學2020屆高三階段測試三數(shù)學附加題]ab1A[A]1a[]cd11134[]．a1A22(，)，(，)lAB33點ABCCl，||?2|22|?4(||2)．ababa2ab2baPABCD，，PC與．PCD6115[(15．已知數(shù)列{}的通項公式為a)()]，*．記nNannn522nSC1aC2aCna．nn1n2nn，S1S28nSn7江蘇省海安中學2020屆高三階段測試三數(shù)學試卷參考答案5．，．．10．．．42．．．．3．．Syx()()，)fxRfx(()在fxRf(x23x)f）0(3)）(3)(2)32，fx2xffx2xfx2x解可得：12；x；x．31，)，，ABCAABAB534A3A1A，A．25A43tanB1tanAtanBtan(AB)，．4B331tanAtanB91tanB4AB則)3，CAB1AB232(21)，115．aaSa2aa121222aSSanan(n1)[(na3(nn2)]，nnnn1nnn16(2,nN)，n(na(na6(n1)aa*n1nn1na}a56n120S2056．2202Snan(n1)n(SS)n(n1)nnnnn18(nSnSn(n1)，nn1SS3，nn1nn1SS11{}53nnS2053，S1240．2021xyxy，yxy(1x)yx0，x22x)4x0…222x21…6x10xx42yy0…21．1x12yy101221．x9，，ABCDABCD1111點E，BB，CCEF//BC，F(xiàn)11，VVAAED1AFED11VVSAAED1EAAD3AAD11119SV，66ABCDACD112AADD11AAEFD的體積V9．1AAEFD14511ABa，BCb，CAc，2，3tanBtanC112311123BtanC則tan(BC)1A135，A1BtanC9B1，B2又，1，BC2B2B5，BC5|c||a|2，sin135552255|，|，ca522524．則||||acca5525(．①()22x1g(x)0，gxx又①，f(x)0或g(x)0xRf(x)m(x2m)(xm0在1xm0則m312m14m04m0又②x(,，f(x)g(x)0()220gxxf(x)m(x2m)(xm0在x(,4比x，x12(i)當1m0m3，m34ii)當m124()當4m12m，2m4即m24m2．(．610）//2ssmnC，ABABCABABAB)C，sinC2sinCcosC1sinC0，，C2C(0,)C32AC(ABCB)18(BC)，113b32SCa3293，22262，2，36ac2a2b2Cc，．M1為PCFM//CD．F2ABCD為E12EA//CD．FM//EA．EF//AM．又，EF//．EFCENPN．ABCDAD//BC，BCEANE，CBENAE．又CEBNEACENE．又F為PCEF//NP．5又NP，EFEF//．CDQ，．ABCDE為//．//．又，//．11，QF，CDCP//．又又，//．，，Q//．//．EF，AC．GAB2BC，為E2．ABCD又DAECDACDAADEDCA．又ADECDEADCDCACDE．由DGC180DGC90DEAC．PACABCDABCDPAC，又PAC．OOM為xONy3x，Q(x，3)(x0)．00|3x3|610由0x0得x3，Q．10500y(xxy60，y3xx3由得即B(，xy60y9(3992，2292km．P，12CPt12AC18t，t)．ttC1PCr對t0,恒成立．222PC2(18t2(18t9)2r2at，當0t110101當t,即t0,時，a72t令gt72t48,t0,，2tt251gt)t48548]t62t0a24548時rPC13b221a2a2，b2，且abc，222ca2x2y21；42）(i)(，B，，設M(2,y)，P(x，)，y011yy:y，0x042y2y2y2(1)xx40，02008224(y8)2(y8)2022由2xx，08y81y120013y04y028yy1x1，0y8204(y8)8y2則OPOMy4000y8y82200O．ii)y18yy8022kPB，0x2y82(y8)2(y8)y02221000由，Qy．0k2MQy02:yy0，(xy02即，xyO．2ak1，ak2，．ak4k456aan1；2ka}，bb2bbn2ban1knn1324kaa…(n3,nN)kaa．①an1aan1n2nn1*an2nn1aakaa．②n2n1n1naanaa①bbnn2n2an1an1n2naaaa22k1bb12，bbb4．b32n12n31a2n2n22ak234k1(1)n；b2k2knk，使得數(shù)列a}na2aa2n12n2k12n1，③a2n2aak2n12n2由akZ，k1．ak4Zk162k1當k13a，a，aZ式，可知a}k123n14aaa2n12n2n1當k2，④5a2n2aa22n12naa2n12nn1nkaa2n2n1故ank1a2n12aa2n12n2n2a}n為2時，數(shù)列a}kna0f(x)x，f(x)，令f(x)0，x1)xf(x)f(x)故f(x))．a），f(x)(xaxaf(x)lnx，x0x1令g(x)ag(x)1，g(x)g(x)0xe11xeeeg(x)0g(x)11g(x)g()a，eemin1f()1a1而，1f(e)2ae2(2ae)，f(e)2e2e2，(2ea)2222ee1a若?0…，af(x)，e)2ex故f(x)在e2121f()11若0f(e)，(2ae)0f(e)，，(2ea)0a2222ee2eee2f(x)在，e2e)f(x)在，e2e)22152111③若?0()0，(e)(2ae?0，()fe(2e)0，aff2222ae2eee2()在(，)()在(，)fxfxe2e2e2e21(，]()在(，)fxae2e2e12當(，)()在(，)fxae2e2ee22當[，()在(，)afxe2e2e2)，()1xafxag(x)在(，)g（1）a0，g(1a)(1aln(1a)a．1e11x11(*)(1)(1)(1a)0．gaaxa1故()在)．由gxax0(x，1a)000fxf(x)xa)，f(x){fa．又f(1a)ln(1a)1x1x，f(1a)(a11a1f即xa)，f(x)a1．at1xt,ta)f(x)a1．:111x11令()Fxlnx1，．()Fx0，xxx2x2F(x)在[1，)1x1F(x)F）0lnx1．x1令G(x)x1，1．()Gx?0，xxG(x)在[1，)161()）0GxG1．lnxxx數(shù)學附加題]，A111111ab1cd1ab即1111cdab12c2d8a2，b3，c2，d1．23A．21)，AB3(,)PlOMP)5，3)5，l3令08C1ABC1)103．23|b||a||ab|2|b|?|a|2，|a2abb|(ab)(ab)2(ab)|22|ab||ab2|?2|ab2|，|22|?4(||2)，a2ab2ba|ab2|?a|，|ab2|?|a||b|2，|a||b|?a|，|b|?|a|217，，為，y，xzA，，(1，，，，，；，ABABDPDC(，．C）PC(，，BD(1，PC與．154102．152814）PC(2，，PD(0，(，y，)．PCDnxz則nPC0且nPD0xyz0，yz0，0yz1，xPCDn，PB(1，．nPB105故cosn,PB．|n||PB|5PCD．）CaCanSC1an12nn2nn1151515C1C()C())n22n5222nnn151515C1C()C()n22n222nnn1811515[(1)(1)]nn522135[(535)()]，nn22151；S151S2353；513535）[()()]，Snn522n135[((35)n2]135[(35Sn2)n)()]2nn52252235353535())()]SS，nn2222n1n即3S，nN，S*Sn2n1n8，8SSSn2n1n1，1，aa121，SCaCa3，3918，SSS1SC1a112122112232S3SS24321，S3SS63855，