41dx）x1xb0aAab1Bab1Caab1Daab12x1,x1fxfx）lnx,x11,x1x1,x1x22AFxBFxlnx1,x1xlnx11,x1x1,x1x1,x1x22CFxDFxlnx11,x1xlnx11,x1x221x1x,y1x1x2ypxyqxy222qx（）xxCDA3x1xB3x1x221x1x22,x0xfx111）,nnx,n1,2,1n0x0是fxx是fxfx在xx0fx在0A與B）A與BTA1與B1TABBAA1與BB1A與TTfx,x,x2在,x,xxxx4xx4xx4xxfx212212323121323123）~N,0pPX2X2）pppp1,A,AEA3123E2次，X2AY2A12X與Y）4xtln1tsintdtlim__________01cosx2x0,y,zxyzixyjzkAxzzx,yfxzy確定，則,v1,（11）設函數(shù)fu可微，由方程xzy2x2dz_________0,1arctanxfxx''01________fa1ax21000100014321,xx,9.5x的2xN12n，r,2r21cos,D22.xdxdyDy(x)y20k.1y'()yx0若yy求'()yxdx0f(x,y)(x,y)(2x1)e,)Lfxy2且fyyxtf(x,y)xf(x,y)t)It)dxdyyLtt)求I222xyz為x123I21x(x)f10f'(x)，f2nf(x)(n1,2...)xn1n(x)xn1nn1limx0limx2.nnnn1112122a1,BaA11aa12B當a011230A00099A,,)BBA(,,),,將3B2B100D23123123,,123(X,Y),0xyxx2yxXYUXY(X,Y)與XUF(z).UXZ3x2,0x,3fxX其他X,X,XXTX,X,X。123123TaT為a41cosx,x0(x)0f在x）axb,x0112()abBab2Dab2C)ab01x1cosx1112limlim,f(x)x0在bab.選ax2a2a2axx0x0(x)()'()0fxfxf）()ff(C)ff(Bff(Dff((x)0f(x)0f(x)f(x)(1)(2)C(1)'f或f'(x)0f'(x)0(x,y,z)xyzf2u）2()12(B)6C)4(D)2fu122{,,}333{2xy,x,22u|u|選vt)/vvt)vms12t）0v(m/s)0530()ts(t(B)15tCt(Dt0000dt,vdt,tt0到vt0001200t0v(t)vdt10t252100（5）設是n為n）E()EBETTC)EDETT(E0(E得)x00ET。TT1E個的即Er得TTTT個200210100021,B020,C020A）001001002()C,CBC,CC)C,CDC,C(E)0A1003rE)1A~020002B0由EB3rEB)2C~C∴ABC,B0P()1,0P(B)1()()PABPABA）()P(B)P(B)C)P(B)P(B)(B)P(B)P(B)(D)P(B)P(B)1n,XX(n2)N(,1)XXi（8）設X12nni1）n()(X)服從分布B2(XX)分布2222in1i1nC)(XX)服從分布Dn(X)分布2222ii1XN(,1),XN(0,1)in(X)(),正確nA22ii1n(nS(XX)(1)C正確，n222ii11X~N(,),(nX)N(0,1),n(X)~(1),正確,22Dn(XX)2~N(0,2),~(1),B錯誤.2n12B41(x)f(3)(0)f1x2(0)6f11f(x)(x)(1)x2n2nn1x1(x)22n0n0f'''(x)(1)2n(2nn2)x2n3f'''(0)0nn2''2'30yyyyec2xc2x)c,cyx1212301i21,2(c2xc2x)ex12xy1(x,y)|xy1aD2222L1aP2Q2,,由積分與路徑無關知【解析】y(xyx(xy222222PQa1yx(1)(1,1)S(x)1nx1nnn11s(x)1x2''1x(1)nx(1)xn1n1n1n1xx)2n1n1101112,,為線性無關的3維列向量組，則向量組（13）設矩陣A，123011,,AAA312123123,,2,,,,rArA2得rAAArAAArA123123123x4XF(x)(x)()(x)2EX0.5x4()0.5()(0.5x40.5)()xxdx(dxFxxEX2222x4()0txdxEX。令，則2x4(dx=242()814()8ttdtttdt2E(X)2.dydxdy2(u,v)2yfexx(,cos)fdx2x0，x0dydxdy2f(1,1),f(1,1),'1''dx2x0x0yf(e,cosx)x0y(0)f(1,1)xdydxfefsinxf(1,1)1f(1,1)0f(1,1)'x1'2'1'2'1x0x0dy2fefe(sinx)fe(sinx)fsinxfefcosx''2x''x''x''2'x1'2dx2dy2f(1,1)f(1,1)f(1,1)''''dx212x0dyf(1,1)'1dxx0d2yf(1,1)f(1,1)f(1,1)''11'1'2dx2x0kk1nnn2nk11411111dx)1x14kkx2nlim)1xx)x)x)x12210n2n22n000k1y(x)y3x3y20y(x)x33y(1)1y(1)03x3yy33y'022'01令y得x6x6yy'3yy3y''0x22x1x1，1將xy1y0y1y10將x將x故xy0y''(201y(1)1x1y(0；f(x)(x)在區(qū)間[0,1]2f(1)0,lim0fxx0()f(x)0(0,1)()fx2()'()('())0(0,1)fxfxf(x)(x)(1)0,lim0ffxx0f(x)lim0xx0f(x)0,x(0,)0f(x)0有x0x(0,有f0(x)f(x)在[0,1]f(x)[,1]f()0,f(1)0f在,1))0f0(0,1),)0F(x)f(x)f'(x)，則使f（）由（1）可知f，，令ff)0(0,),使'()0))0fFFF，(x),)在對F,),'()F'()0F且12121212F'(x)f(x)fx)f'(x)0在2xyz22xSz22為9xyzC222()xOy求C在()求S的Mzxy22xy2x（1）由題設條件知，C222xz22xyx22則C在xoy0z(x,y,z)dS9mxyzdS92xy2dxdy22222ss:x2y22x18d2cosrdr264202A,,（20）（本題滿分3有31232。312()2；()若Ax11231k21R11220,,312123123A0A123A1個1,0A2120))2∴)23)1Ax01111220,,22A20Ax0由又，12313111111,,21A111，123131111k21R11)2xxax2xx8xx2xx212223123121323XQYy21y2a的值及一個正交矩陣Q212111326122;Q0,fx3y6ya212236111326214f(x,x,x)XAXA111T12341a(x,x,x)XAXyyf2122，T12312214故r()2|A01110a2，41a214將a2r()22A111a412214|EA11106，1234121(3E)x01；由A111(6E)x0A60由211(0E)x0A02由313P,,,,6令P112312301111,2,1,T，11,1,1,1,0,1,TT32623111326312則Q016，QT36123011326xf3y6y2122,Y（）（本題滿分分）設隨機變量X相互獨立，且X的概率分布為20y11P(X0)P(X2)，f(y)Y20,其他()PYEY)求()ZXY求,0z12,234z(I)YEY};(II)f(z)9Zzz231()EY)y2ydy02492PYEY)PY)2ydy330()F(Z)P(Zz)P(XYz)zP(XYz,X0)P(XYz,X2)PYz,X0)PYz2,X2)11PYz)PYz2)22z0()0FZ0,z20當zz3()1FZ21,z1,z即當zz1z20z1FZ()2z121z2()FZz112z3()(z2)2FZz2201z0,0z1z221(Z),12zF2z11(z2),2z32221,z30z1z22z3z(Z)F(Z)f'zzn次,XXnX12n(,)in)nZX布N2iiZ,ZZ。12n()求Zi()利用