高二数学选择性必修二同步练习与答案解析(基础训练)

52,22,222,2222,）210n1D．108B．101210n1nn9）1,2,3,44,3,2,1与C．a216项a8项）nnn7项9项）aa*nn6）aa42，12，206）nna4n222(nannnnna32n1a2n1nnaan）Snn2n4n96）第1行第2行第3行123456711n1a,nN4）an2n112211a，a1(na2014a）14nann1144557461,3,5,7,9,aaaannNa9…2n12nnaaSnn12nnn57214n12n337fxx2xnnNbfaaanb，2*nnnna=nb=na1a121anSaa，nn33n1n1S125nn,nNaaa2*nnna}nS2n30.n2nSnna}nnaa1,aa.nn1n1n1a5nan33，aa22a和aaa1.nn42n10aS2na(nN*).nnna,a,a,a,a1；2345an52,22,222,2222,）21210n1D．108101nnn99,99,999,9999,101，n291．2,22,222,2222,ann）1,2,3,44,3,2,1与C．ABBCa21a8项）nnn6项7项9项令25721.n8naa）*nn66424a，6）Aaa42，12，206）nn4n2a22(naannnnna32n12n1nn1012aA31662220aB4112,a226,a33a44a，22221234故C951412aD3aan）Snn2n4nSS8a．2244396第1行）1第2行第3行234567n2n1，21n∴第八行的最后一个数为21255，89611n1a4,nN）an2n112211n1,nN，a2nnaaaa0．123411a1n(aa，a）14a2014nnn114455141a}n，a1(n，aan1n11a125，1414a155，3114a144，53a}n67131，1aa．4201417461,3,5,7,9,(1)(2n1)，(nN)an1n1,3,5,7,9,，(1)(2n1)，(nN)an1n(1)(2n1)，(nN)an1nannNaaa…a2nn129a...a64当an8①128a...a81n9当a②129a9nn1anSa2nnnn1a2nn2n1aS1313，当n当n当n112nn1[(n3(n2n4，aSSn22nn11242a，1n1a2nn2，nn1a2nn2n57236，，3，，5，6，7，4123；6.14n12n337173n131113；33令nn233n132n73令n7771；.73fxx2xnnNbfaaab，2*nnnnna=nb=nn1n3n32fx当x1an1f(1)12nn1；nfx将xn1bf(n(nnnnn3，22nan1bnn3，2nna1a1213aSana，nn3n1n1S1215323b243ba1ba1bb2b，，nn33n1n23241b1ab11；b33124343a1，bb2b，bb，n1n32312nn116aa6321an5.nbS3221212n135nn,nNaaa2*nnn(3,)(n1)，aaann(n1)2n2n1n(2n1)3.，nN*∴(3,).a}n2.nSnn2nSnna}nn7或n8a4n32n1522522n30n2(nn)2nS，2222nnN，+n7或Sn8nn1，aS211当n2SSa，2nn[2(n30(n4n22nnn128当n1a14n32annaa1,aaa.n1n1n1na的前5nan111111,a,a,a,aa2345n12345nn1,aana1n1n11112211a2a1，aa，11222，a4344411a4a4.3141545351ann3232a1aaa和a，a.nn24n10n2aa,.4nn3d2c4c33122d4c，d2,∵a，aa223424n2n24n2a∴a.4S2na(nN*).nannna,a,a,a,a1；2345an32748a1a.，a3，a，a.124521n,N*an2n1n1aS2an，a1.111132aaS22a，a2当n当n当n当n，1222273aaaS23a，，a123333445aaaaS24a，a，12344448aaaaa25a，a.12345552111a，113212a2，22217213a3，4231214a4，，8241215a251521n,N*.an2n1n5aa11d2a8）naa24a8a（24，）n816168aSna4,a2S）nn245aaa0a（2）n147）a7Snn47aa5aa3，）1n1nn1n2n2n1na11a（7a5）nnnN*）nn11n4n3818第8斤斤n）斤斤aSSS,SS,SSdnn545676）0a06dS和SSSS856n4746与212+12a}da0a1，n11SanS10,aa6dnn526a}na11a5，a5d3a3SanSa3a11，nn1554为3aaa3n1n5anSa5a11，.nn25anS120n.naaaaa36Sn251215a20S11667nnSnSana7S15，．nn13anSnaa8aaa，.n3724an1bbn.Snannnn5aa1d2a8）n1aa7d17215,81aa24a8a（24，）n816168aaa2a，16n824a8.24aSna4,a2S）nn245aaaa42615245aa56S15225C2aaa0a7（）n14aa2ad02a3d1411aa6d3129.71a7Sn）n47aS7a35.n74.Caa5aa3，）1n1nn1n2n2n1naa3a5n1nn53n13n2,nN则a.*na11a7a5（）n51aaaaa5a252，da352123453aa4d13故．73nnN）*11n4n3nna5,a83，d12a5(n1)33n2，nnnN设k*则n11k2，kn3，818第8）斤斤斤斤adnSn，an187Sad，281a65aa81d184．，181aSSS,SS,SSndnn545676）0a06dSSS和SS856n4SSSS0a0由由，54545SSSS0a0B56656aad0a00，dA6550adSCnnSSSS0a0由，76767SSaaaa2(aa)2a0SS8D84876576747462+1与21221212.2+1与21222，aa}d0a1n112，a}dnaa10d0，111，a1SanS10,aa6.dnn526a34S105由有aa626nad31d1a2d21a}a11a5，a5dn39a}na11a5，3，aa2，d312a4d189.a51SaSa3a11a3n，n155n2043a2aa4；a2153355S(aa)225154;20.4为3a,a,...,a1a,a,...,ad29129aaa4aaaa3aaaad4，，12367891231987aaaa4a26d3S9ad，da126789191；aaa3n1n15n7.；8,13,18,23,28,33,38.ana8,23,38na81空空；aa(nd8(n1)1515n7.n1715n5anSa5a11，.n25nanS120n.na2n110.naa，dn1a5a11，，25ad5a4d11，，11a3d12.，aan1d32n1n1，nN，*n1aa2n1，nN.*nna3a2n1，，1nS120，nnaa，1n232n1n即，2n2n1200，210n.aaaaa36S16n251215a20S116144.220aaaaaaaa2aa36，25251aaaa18S；11162211aa112aSa11.1622667nnSn4daa5d235d0，61aa6d236d0.71235236d又d.Zd4.0adna0a0，，67656S664.nSn2Sana7S15，．nn13anSna2n916．nd15ada．n1a7d12a2n9a由得．nnSnnn4．22n4Sn16．naa8aaa，.n3724an1bbn.Snannnnna2n2n2naan1dad.nn1a8,28a1d3，aaaa6dadad172411，da42，1aa2n2.nn11111bn2nn1，na2nn1n111111111nS1.1nn2n12n2n222335aaa1a4，（）3n15222a16aaa，14nn12122aa1q21，5）n）23与2311或1723盏）盏盏盏）111,q,a,a}an122nn）xa}nS,a2q2Sn）n250a中，2aa2a0列bba，2nn371177bb68则（）10a）10910a410a410a910a55746a3a2a且aa221n34qaaa2aqn2431313LL1LLnnaaa6a8qa，123nn61a18S26Sanaq，1nn33anSa1SaSaa，，a，36knn136nk5aa2n6nN*.nnaa，；25aa，bb1225nnanSa2a8，.n13nanan.Snna}a164aaa，．a2312na}nnS（2）求数列{}．annn1a,a,aaa1139nan1Sn.aannn1a}nnSSa0，2.an221a}nSa48nnn5aa1a4a3，（）n1522aa1a4a，aa4以a232n153152a16aa，an14n11222qaaaqan1nn1naaq162qq2.3341aa1q2，15）naa1q2，51na1q11121255S31，1q523与23）11或123与23，m11或m1.则m2m723）盏盏盏盏1xx31x(1)5，S113x243，1()23111,q,a,a}an）n122n11n5aqn5an122n1x）qx16xq0，22∴x4，a}nS,a2q2Sn）n25aa11a}nS,a2q2n2qn2a1qn11q1125Sq131.S12n50a中，2aa2a0列bba，2nn371177bb68则（）4a0a0a4,或aaa2aa2n377777aa4b，0n77bbbb2n68710a）10910a410a410a910a55nan1ann1a1a10a1010n10n1nan1aa1n10119aa1010即a910a746a3a2a2a且a2134n43a33a2aq4.234a3a24a233.1q243a2aqqaa243naaa2a，243naq2aq121qqaq132q2，11131LL1L3Lnna}n，n22222a}()()()，an1n33333nn2n()，Ln3n5，5．，qaaaa6a8n123n22naaa1q62a121q0aq8，a12q231q0aaq222n1n1n.n12；.2n6111111na}na}n22111a6a，2n26n11n由a得n1011.2nn116经过111；11.Saa18S26anqn331n3当q1Sq1；a33aq1821a2当q1a1.q31q32611qaSa1Saaa，，Snn，ann13636kknn22Sa3a3da5d3d1dd1，由d得3611n(nnn2nSnn则a，．n22aa26由，，aaa，a363kk即6kk12．2nn225aa2n6nN*n.naa，；25aa，bb1225nna2a4b(.，n25na2n6nN*na2a4，，25bba2ba4，，n1225b2bq21bq(2)(2)(2)bbn1n1nnn1anSa2a8，.nn13ananS.nn2,nNS2nNna.n*n1*naaq2q8q2或q2aq22n31aq2a，nN.*n1nn1a1q121212nn22.aS2n1n1qnna}na164aaa，a．3212a}nnS（2）求数列a．}nn1nn2a2n12.nSn2nq(qa}n，aq161a231．aqaq2(aaq)q221111222数列a}an1n；nn1nn212121nnn.Saaa12n22n122n12n1a,a,aaan1139an1Sn.aannn1nannSnn10ad（dna11a,a,a139aa(12d)1(18d)，a22319d1，d0ann，1111n(n1)nn1，aann111111S1+n1nn2231n1n1n1a}nnSSa0，.a2n221a}nSa48nnna26.n1naaqa2a02，Sa02na21211a11aq2又a.a2n1n12n1a1q1na21232121SSn1n1，nn1qnnn3n6，由3214832492n1n1n1n45a（a）a(1)(4n1)aan1nn1051111，，588n1)nn）25nnnn1n26n46n4n2111aaaa（）a，a6a2aan2612232021）491n1n12n(nn(nn(nn(n11n1n2222ann）nnnn22n21aa=5，a=3））naan53n1n112,,1222,nSS2nn2nn42n2n2n1n41111n1n2n1,2,4)2481n21121n1nn1122n2n111n112n2nn1212222nn2n1an)aaaa()a2nn2123202020212222123104x2f(x)，ffff()111111114x7461naaaaann12nnN，S2020an，Sacos()n*nnaaan29nnnn1a}a}aannnn1aa11aaa1，，dn241S100daann1aaa5aaaan，是与n234281111aaaaaaaa20191223342020Sana12a2a2an2na2n12nn23nnSn5aa17a，．a35n6an2bnbSn．n(a3)nnna11a,a,aan139anaT.nSnnnnannSa2Sn1nnnanSnT.nna}nnS0)d(dnS5(a1);a,a,a②S5126a；n1abnT.b2nnnnnq1a8.2aa,a1n3annbnbn.S，annn5aa（）a(1)(4n1)n1aann105，a(1)(4n1)n1na(n1(4n(n((，n2n1ann1则……a)a4565，aaa(aa)(a1111，，n）25588n1)nnnnn1n26n46n4n21111∵∴(3n1)(3n2)33n13n2111Sn2558nn111113255811=3n13n2111n=323n26n4111aaaaaa6，2（）aaan2612232021ad21，d1，aa1da5d6n111111a1(n1)1n∴，aann(n1)nn1nn111111111120120212121aaaa1223∴.aa12232021491n1n1）2n(nn(nn(nn(n11n1n2222当n1491n1n372n12n(32n1)n(n1)2149161n1n222当n1491n1n372n11n22n1[32(n1)1]2149161n1n+n222n(n491n所以1n122n(n1491n1n1n122ann）nnnn22n2nSnnaaaSn12n222132n1即S2nn212(2nnS122n22n故Sn12n1aa=5a=3，）aann53n1a545a1da1a1设则则d5得，a3a2d311dn3an．n1111nn1．aannn1n111111111223S20191112,,1222,nSS）2n1nnn42n22nnn4n1n22n11Sa1，当n11214311SnnAB11S2121112141n1SC1112121n1SD11111111,2,4n)2481n21121n1nn1122n2n111n112n2nn1212222nn11111)248n1＋11)24n121()n]n(n21＝＋2121＝122n1＝122nC2n1n)(aaaaa1a)2n2n232020202122222n1an)22naaaa12320201234...2019202022222222143...222221234...20192020122123104x42f(x)，ffff()11111111x4xxf1x1fx4242xx11110112956ffffff5.111111117461naaaaann512naaa1234567891012515,5nN，S2020anS，acos(n)n*nn0cosn2cosnaacos(n)an由得，n2na以2nacos1acos1又，，12S1010aa0.12.0aan2a81949nnnna9nS12223292，123992S12223292，2341092129S222123292109928221010，129S822.1098194.1a}na}aannn1na22n12n.n11111b设则则n.Taan2n2n24nn1nnn111111111nT1…1.nn14n14n1n4223T202041aa11aaa，，dn1241S100daann1aaa∵，，d)21d)d0d1．aaa，22124141111an∴∴，aann(n1)nn1nn111111S)()()．100223．a}nb}nab}nnn1{}（ka0nnaannk{paqb}nnaaAm（Anmaaa5aaa是与an，n234281111aaaaaaaa20191223342020naa5aaa由且是与234282ad51，adada7d2111，ad11aa(ndn，n11111n(n1)nn1，aann1111111111122320192020故aaaaaaaa20191223342020112020，n；n2a2a2an2naSaa2n12nnn123nSn2n12n52n12n1a2a2a2an2n，2n12123n1a3，n1a2a2a2an12n1，2当n22n2123n12n1a2n+1aa3，12n12nnn12n1a，2n1n12111n1012++2n+13+5+7则S，222n1则S211122131++2n+1n3+5+7，222n11121n11nS3+2+2++22n+122222n1112n521nn13+2n+15，212n122n5S.2n1n5aa17a，．a35n6an2bbSn．n(a3)nnnnna2n1.n1na，dn5a2d5a3由1aa17a16d3ad611a1,d21，aa2n1;nn2211b，n(a3)2n(n1)nn1nn11111nS1....1nnn1223n1a,a,aaan1139ananSn.Tnnn2nann.n10d,d，a11a,a,a由则13912d1d112d1d或d0aan1d1n11n，n1ann故a.n，annn1n2nn则S22n112212nnnn1nn1S2n11111T212231nn1n21n1n1121n1nn112n12nn1anSa2Snnn1nnanSnT.nn2aT22n4nn1nna2Sn2a2Sa2a(n2).n与n1n1nn1n2aq2，a.21a2S2aa21又，2112n∴ana2Sn122，n1得Snn2nT22…2n∴n1232122n2n22n4n112a}nnS0)d(dnS5(a1);a,a,a②S5126a；n1abn.Tb2nnnnnnn212an2n；（2）T22nn9S5a1a11d591ada；121aaa2adda5ada﹔aaa，，a，d2222126216111115aaaa2d7；S5a1552313a3d3an2n、﹔11bn2a，2nnn1111[147n()则T2222nn23121(1)2nn(1n2)n21n2，1222n12nn212即T22nnq1a8.2aa,a1n3annbbn，nS.annnn2a2nNn1Sn12nn1qa12，1aq815q20a4∴2q2∵q1a2nNn1a.n1q2nn123S，∴nb2n12224232n1nn121222n1nSn2n12n234121111nSn2n12n22222341122nn21111nn1S+n221∴=12222n12n1123nn125123...2nn2n1nknk1到）2k221k2k12k2k1k2...2k1111nnN,n1）*2321n111212B．122311111131423234*1an21aaaa1,nN1n2n11a）B．1aC．1aa2a2n2n21123nk1nk的n22）12kk12k21k22k1k2k1222213512n11nn，nNn*n1nN）*11151nk到nkn1n2n6）1111111k1k2k3k1k2k3k111k1k3111nkn1n2nnnk1）12k111，2k12k11Ak11Bnk111111211n2n1234k(k2n1n2n4n（）k1nk2n2k2n2(k2)nyxn1nxnnnkkN*nkkN*n2k1kN1)(n2)*n2k1kN*(nn)2135(2n1)nN(nnk到k12k22(2k1)(2k2)2(2k1)2kk174611231n2+2n2k12．用数学归纳法证明关于nn1427kk1kk1n2k111111111234nN1*2n12nn1n22n1111111112342n12nn1n22nknk1nP(n)nnn111111111…2342…“n1nn2n42nkk2k（且nnn3anNa1aa*n1n1nn3n511111111234nk到nk112nn1n2n32nn,4nn1912aNn2,n*aa，.a2n113nna、a；32ananS2San,a0a2nnnnnn1且ana11n1nnna，，a；a234n5123...2nn2n11knk到n）2k221k2k12k2k1k2...2kknk1到nkk1232212112322122kkkk，1111nnN,n1）*2321n111212B．122311111131423234∵nN*，n1，∴n2213，112231．*1an21aaaaa1,nN1n12n1）B．1aC．1aa2a21an2aaaa1，12n11a1n11aa11aa.令n2nn122nk1nk的123n22）1k1k22k21k22k1k2k12222k当n当n12k，2k12，k112kk1k2222k1k2k3k12．22213512n11nn，nNn*n1nN）*1nNn*nNn1*1nNn*1115nk到nk1n1n2n6）1111111k1k2k3k1k2k3k111k1k31115k当n当n，k1k2k61111115k1，k2k2kk1k2k361111，k1k2k3k1111nkn1n2nnnk1）12k111，2k12k11Ak11Bk1111k当n当n，k1k2kk111k1(k1(k2(k(k11111，k2k3kk2k12k1111knk1n，；2k12k1k1Dn111111112342nk(k2n1n2n42nn（）k1nk2n2k2n2(k2)nn成yxyn1nxnnnkkN*nkkN*n2k1kN*n2k1kN*2k1kN1nn．*(n1)(n2)(nn)2135(2n1)nNnk到k12k222(2k1)2k(2k1)(2k2)k1k当n当nA(kk2)(kk)(kk2)(2k)，k1B(kk2)(k1k1)(k2)(k3)(2k2)，B(k2)(k(2k)(2kk(2kk2(2k.则A(kk(2k)k174611231n2+2n2111222341211122234.21112223412k12．用数学归纳法证明关于nnk11427kk1kk12n427kk1k1k4k1k212k1当n1427kk1k1k4k，1k22，nk11427kk1k1k4k1k22.427kk1k1k4k1k212.nN*1111111123412n12nn1n22n11122nnnNn1*12121，111．221111111123412n12nn1n22nknk1n111112k112k1221111nknk1当n22112k112k1P(n)nn1k2k1P(n)nn2k112k1nk1k1；2k1n111111111…2342…“n1nn2n42nkk2k（且nn11112k2n1222421111…234111112…对在nn1nn2n42nnn2，111122kk2k且2当n1242n（111111111…2342…k1kk2k42knk21111221k2当n2242n3aa1nNaa*nn1n1n3nn2n324n352a1a1a1，aa14a15，；an1nn32221a2a128a，2433123(32221a52a3a，，，442414nn322a4a44n1a11；nkk32kna，4k当nk1k3aa1k1kkk3k(k3)21k4k6k9k4324k4k2k9k43224k(k4)(2k1)(k4)24(k4)(k2k1)24(k1)(k4)2,4nn32a，4n3nn2；24511111111234nk到nk112nn1n2n32n11111；2k12k2k12k12k21111nk1234，2k111111k11234，n2k2k12k211knk1到n；2k12k21111nnk，k1k2k32k111111k1，k2k3k42k2k12k2111.k12k12k211111；.2k12k2k12k12k2n,4n19n1415n1189nn1415n19nnk1nk415k19kk144k1kn4k19kn,4n19n12n2,n*aaa，.n3na21n1a、a；32annN*3445n1n2a，n34a3a，；452n22aa313nnnk当nk1∴nk1a，kk11，k1211kkkna.*nan2San,a0S2nnnnnnnan，∵①nnaa12222nnnn2a1122∵，，∴∴．1且a11na，，a；a23432aa，，．n234n1a1n31517，aa2132431nnn1a112k1kakk11kakkk1nNannn）fxmxfx1fx）00x0x01mm(3,3t)t3s）296t(t)6tt(t)29t2tf0fxxe2x（）42D．10,f2f2xf2xyfx2xx0）4343fxyfxxfxxx（在）0002xx012lnxy）11ee2xxP(1,2)y2））2x2(sinxcosxcos2xxx11xxx21xxax1(1,a2)ya）42612746xlnx2xyysinx2cosx,211f(x)x2xff22(x)2x3x5x4()f(3)fxf32fx2fx1ggxg1fxxxxbyf(x)xg(x)ebxkk53cosx2x43lnxy3xxlnx在x1yf03001320f，fxaxbxcxdff32，，ad2(x)(x1)eax00xybfxx0yx和e1(0,2)yy2x5Wt）WtWttWttWt乙t在，0甲00甲0乙0tfxmxfx1fx）00x0x01mmfxxfxfxxfxmx10000，xx0x0x01fx.0mt)t3(3,3s）296t(t)6tt(t)29t2ts(3t)s(3)(3t)333t(t)222.fxxef02x（）42D．10f012xexfx，,f2f2xf2xyfx2xx0）3434f2xf2x2f22，xx0,f21yfx2f21，.4fxxfxyfxxx在（）002x0x012yfxxx在0fxxfxfxxfx1112fx则.00002x2x20x0x0lnxy）11ee2(m,n)，11，mlnxy'由yx1n(xm)y，m1nm)n1，因为切线过原点，所以0(m,n)ymlnxnlnmme，1，exxP(1,2)y）2′2x1，yyxx2P(1,2)2113.xxy2）2x2(sinxcosxcos2xxx11xxx21x22ln2xx(sinxcosx(sinx)cosxsinx(cosx)cosxsinxcos2x221x)xx2x1xax1(1,a2)ya）42612xax1y4x2ax，由y423xax1(1,a2)4286yaa.42746xlnx2xy3x-y-1=0f(x)xlnx2x，f(x)lnx3，f13，y23(x1)，即3xy10，3xy10．ysinx2cosx,2xy20由y得sinx2cosxycosx2sinx，ky1，cos2sinysinx2cosx,2xy2xxy20.xy20.f(x)x2xf1f12f(x)x2xf12，，fx2x2f1f12.f1212f1.22当yx)121222225k＝1xx1当y12122k＝2xf(x)2x3x5x4f(3)f(x)326x6x52fx2x3x5x4fx6x6x5322f36(3)6(3)5312fx2g1g1fxxfxgxx12ln2x21fx2xfx2ln2f12ln2，x，gxg1fxxgxg1fx1，g11g1g1f112ln2g11.211；.2ln2x21yxbf(x)xg(x)ebxkk1(1,0)yxbb1；x)1x1f(x)xe1g(x)(k,k1)g(x)e又exk，xkxkxk得k2．53cosx2x43lnxy3xxlnxy在x13x6x4y2xx3x6x4y；2xxylnx1y(1)1；f03fxaxbxcxdf00f13f2032，，，ada1,b3,c0,d3fxaxbxcxd,32f(x)3ax2bxc2f03f003f20f1由d3c0;，ab3a1a1,b3,c0,d3.fx()xx33b33212ab02，00041k=211=，0021，1241即142(x1)eaxxybx00f(x)x1,b1a(x1)eaxf(x)e(xeaxea，由f(x)x'xxx(x1)eaxxyb0，f(x)x0x1a1，a1f(0)'(x1)exf(0)(0e01f(x)，x0(0,1)，01b0b1，1,b1ayxe1y0y(0,2)和2x132，ye(2)2e2x，2xye0x0e1y(0,2)y2x2.2xy22x22A33x2x2y与y，,2x2y与xB，121330,yxy2x2和yAOB1.225f(x)f(x)））yxcosxx4y2x12yyx1xxf(x)）220,0,10,12xy）2x,0,1)(yfxyfx）,12,0,1,,fx2x2lnx）11120,,0,和22121212,,0,和xexy）(x)f(x)ffx与fx的图象如图所示，则不等式组）0x330,11,2(x)()()fxxfx()0xRfR）fffffff(1)f2222fxxalnx132在a）2,182,18,218,7462x6x11y32fx5xx0f(x)2xax在)a的最大值是_____．a3fx2x6x7f(x)232x(b3)x上的偶函数，则实数b2Rg(x)x2(0,)在x(x)xlgxff(x)f(x)ef(x)af(x)f(x)是xx[2,2]a5fxx3x3x(xf(x)xfxeax1.xa2fxfxRafxxax13.)fxafx(1,1)a.5f(x)f(x)）,1)(4,)(1,4)，∵f(x)在(1x4f(x)01x4x或f(x)0．）x4y2xyxcosx12yyx,00,AyByx42在RxyxcosxCy1sinx0在RR0,12D在yx1xxf(x)）220,0,10,10,1xx由f(x)，221x211f(x)xf(x)0x1或xxxf(x)2xy）2x,1,0)(22x23y0得2x20x1，y2x3xx222xy().2xyfxyfx）,12,0,1,,2x0()0(2,0)(2,)，．或2fx()fxxfx2x2lnx）11120,,0,和22121212,,0,和1fx2x2lnx(0,)()4，fxx，x112()0由fx40xx，x1(,).(x)f2yxex）y(x1)ey0x1()y0yxe在'xx1''x(,1)f(x)f(x)fx与fx的图象如图所示，则不等式组）0x330,11,2f(x)f(x)f(x)f(x)解集是{x|1x3}．0x3Rf(x)f(x)(x)f(x)0xR）ffffff(1)ff2222FxFxxfxFxxf(x)f(x)0令为RF2F12f2f1即，fxxalnx132在a）2,18,218,2,18axfxxalnx132x∵f'x，在23a03故2x在a2x在2x∴2a18.7462x6x11y320,2y6x12x6xx20y0x2，20,2.0,2fx5xx20,5fx0,，25x2f'x5，xx25f'x00x令，22fx0,0,.5在50f(x)2xax在)aa3aaa1a6．f(x)6xaf(x)0x或x6266fx2x6x732,02,和0,2f'(x)6x12x=6x(x2)f'(x)00x2，2'(x)0x0fx2x6x7(,0)(2,)令f或x2,上32(0,2)x(b3)xR上的偶函数，则实数bf(x)22g(x)x2(0,)在x2,fxRfxfxb3)xxb3)xb3，2，x2x2x2gx2，1xx22gx0令2，xgx2,.2,f(x)1.xlgxf(x)f(x)1,ee11xlgxf(x)xxxlgelg.f(x)xx1令f(x)0ex1x.e1x0f(x)又f(x),f(x)e1x,f(x)0当,f(x)e11,eeef(x)af(x)f(x)是xx[2,2]a1af(x)e4exxfxeaefxeae则xxxxa1f(x)是[2,2]f(x)[2,2]ae在exx2,2][2,2]e在2xeae0在[eayxx2x1以a.e45fxx3x31,1fx3x3，∵23x301x1.2fxx3x1,1.3x(xf(x)x，【答案】增区间为(0).1fx·xxx'lnxx'x1x由得，，xf'xx2x2x2f'x01xxe令0，得1x0x2f'x01xfx，0xe时x00e，令x21xfxe.f'x0ex令0x2fxeax1.ax2fxfxRaln2,,ln2fxa0221fxexxafxe2，则令'xfxe20xln2'xfxe20xln2令'xln2,fx,ln2fxRfxea0'xfxea在e0R由'xxa0a0则0fxxax13.)afxfx(1,1)a,3fxfx3xa)2fx0(在)3x2a0,3)a3x在(aa32fxxax301fxxa.a32aa由f(x)0x，33(fxaa,)，33(1,1)，fxaa1,1)，,)(33(aa3.13.当．，．②当，，．③当④当．，，，，，，．分①当．，分当．②当，，．分③当④当分，，．分35是区间[a,b](a,b)）f()fx()fx()fx[a,b]()fx[a,b]()）2alnxaxx在f(x)（）12abfxfx13处的切线