2022考研數(shù)學(xué)一真題及答案11

4fxx21ax與gxx0x〕116AabBab..611Ca1,b.Dab.66A(x)xsinax,g(x)xln(1bx)f2f(x)xx1aa2洛洛g(x)xbx)2x(bx)22x0x0x0x0x0asina23lim1ba3b,BC。bax01acosax1acosax0x0lim故a1.D。bx2x0y,yx1,yxcosxdxdy，1Dk，IykkDkD1maxI4〔〕x1kk4CI.DI.AI.1BI.234D,Dxf(x,y)yxf(x,y)y的24I0I;24D,Dyf(x,y)ycos(x)yxf(x,y)132y0；xI1(x,y)yx,0xI2y03(x,y)yx,0xfxyf)xftFx〕0f)Of)0x1123100xx23123A.B.f)f)1100xx123123C.D.Df(x)xyyxxF(x)0()0①x②x③x④xFx()Fx()Fx()0Fx。D,blima0〕annnnA當(dāng)babB當(dāng)babnnnnnnn1n1n1n1C當(dāng)babD當(dāng)bab2222nnnnnnn1n1n1n11b(nA取annn1bB取aD取annn1bnnnlima0,N,nNa111nnnb1blimb0,N,nNnn22nnn1NNabbab2n22212nnnnnn111,,,,3是3R23123123,,〕122331101120A220.B023.033103121416121411221124111DC..644111461166126,,,A，那么A稱為基,,,,【解析】因?yàn)榈?2n12n12n,,,12n11,,,,到M2312312233111,,,,M2312233112310111,,22023123033A。,B2A,B*,B3AB*OA〕BO32B*OB*OA.B.2A3A*O*O32*OA*OC.D.2B3B*O*O1CCCECCC,CC11C0A0A（）AB23620B0B10B0A0A0A06A1BB160B0B001B10AA130B02B6130A0A2x1xx0.7XFx2〔〕0A.BC1D.0.3.0.7.Cx1x0.7Fx，22x1Fxx，2x1dxxFxdxxxEX21x0.35x2x11u221xxx0udu2而，dxu2200.3520.7EX?！?〕設(shè)隨機(jī)變量X與YXN，Y1PY0PY1FzZ2ZFz〕ZABCDBF(z)P(XYz)P(XYzY0)PY0)P(XYzYPY1)Z1[P(XYzY0)P(XYzY1)]21[P(X0zY0)P(XzY1)]2X,Y1F(z)[P(X0z)P(Xz)]2Z1z0F(z)(z)2Z1z0F(z)(1(z))2Zz04zzf,2,vfu。yfxyfxf"12'2"22fxyfxf"12'2"22zffy'1'2，xz2fff"'2""'2"yx0yyCCxe12yxy000yy。xex2yx(ccx)e1a2,b1yx1212y2yyxAxBy',A1y*2ABx2BB2x2y*()2yccxexx12把y(0)2y'(0)00,1，cc122xexyx:yx0x2xdsL。2L136x,yx,0x2x2xy14xdx，2212x14xdx214xd14xxds2228L0012136214x23830x,y,zxyz1zdxdydz2222。415sindd21z2d222000d12dd240001432d350zdxdydzxdxdydz2ydxdydz22112dr1xyzdz22224330001sindsindrdr列向量,2，其中為T(mén)TT。2T2,TTTB,pX和S2,X,,XX12mkS2np為kX。21kSX2為np2E(XkX)np22npknpp)np21k(1p)pkp)p1k1(x,y)x2yylny9f22f(x,y)2x(2y)02xf(x,y)2xylny102y10,y故xe12,4fyfxf22y12(2)fff1e2xx(0,)exy01(0,)eyye1(0,)e0()0fff而f2xxxyxxyy11(0,)feeyxnx9ay與n1nn記Sa,SaS與S21n22n11n1n1xy=xn+1x0和x1與yn111111a(xxdx(nxx)n1n1n2，n01201n2nnn1111111NSaa-))23N1N22N2N1nnNNn1n111111111111)23456Sa（（2n2n2322n1n1n11xnx(1x由2n(2n111ln(2)1()1SS1ln223422xy22S1x繞S4312xy224,01x43S及S12S與S21xyz222S1，4311xy221yx2與，43212zx2Sy2。2221xyx222yx21y31，2434121434y2y4x2x423x那么V2122224000011434243xxxxx32312400fx在aab,b(,)a,bfbfafbafxA，lim00fx在xx00A。0fffb)f(a)ba(x)f(x)f(a)(xa)(x)，易驗(yàn)證()()(),,ab；x在閉區(qū)間ab上連續(xù)，在開(kāi)區(qū)間ab內(nèi)可導(dǎo)，且fb)f(a)(x)f(x)。''ba,b)0a內(nèi)至少有一點(diǎn)'fb)f(a)f)fb)f(a)fba)''ba(0,)()xfx00,x0,x00f(x)f*0,x0,f'0x00000xAlimx0fx00'f(x)f0f0limlimf()lim)fA'0''0x000x0x00000(0)f(0)A故f''。xdydzydzdxzdxdy，其中I23xyz2222x2yz4222(xyz)2x2yz4I2222222xyz2x222(),①x(xyz)(xyz)22222222yxz2y222()),,②③y(xyz)(xyz)22222222zxy2z222(z(xyz)(xyz)22222222xyz()()()0x(xyz)y(xyz)z(xyz)2222222221:xyzR.0R2222有161ydxdzzdxdyxdydzydxdzzdxdy13Rxdydz3dV(xyz)R3R3R32223/231111111A111設(shè)12042A的.2A2,.321312,,,32312A21111111111111,1111000002111042202110000r()2x20x1,x1Ax321x0x13x1210k10故k211212A31220A2220440111022012A,220100002144020000x1Ax0x1,x0得213111220k10k故2322000121kk12111kk2kk(2k1)(k)2k(k)k(2k1)22121212122122k10110,,故21232,x,xa1x2xx2xxfx212212331323fya2fy212a01A0a111a101a10aa|EA0a1(a)1a1111)[()(1a1(a1)1][0()]aaaaa(a)[()(1)2](a)[22]aaa221294(a){[(12)]a}2(a)(a2)(a1)a1,