2006考研数一真题及答案解析

word格式--感谢下载支持164..xx)）lim2.1cosxx00.0xx)1cosxxxlim2.lim1x0x0x22yx)）yyCxe(x0).xxdy11dx，yxlnxxClny1yCxe（CeC）x1zxy(0z1)）设22ddz2zx3(z1)dy2.z1：y11x212.z1(xy1)设：221ddz2dzdx3(z1)ddyz2zx3(z1)dyz2zx3(z1)dxy.11＝6dv6drdrdz2，2zx3(z1)dy211而ddz00rV1ddz2dzdx3(z1)ddy0.12zx3(z1)dxy.z4y5z0d）点3x2.d000ABC222000d222EB，为212AX.11.11XY.XYXY,.则PX,Y1PXY1PX1PY1221x.01SX,Y1PXY1阴则P.－4..f(x)xy，x0x00yy..()()0由fxfx()fxyf(x)yf(x)x000d1f(rcos,rsin)dr）设f0022x2f(x,y)dy2.）20x0022y2f(x,y)dx.y.[20y00.DYdyy2f(x,y)dx22.0y.ann1）nnnn1n1aaaa..[Ｄ]nn12nn1n1n1word格式--感谢下载支持由aaaann1nn12n1n1n11(n取ann1(n取a.nn与(x,y)（）设f(x,y)(x,y)0(x,y)0f(x,y)在约束均为可且知是y00(x,y)00f(x,y)0.若f(x,y)x00y00f(x,y)0.若f(x,y)x00y0000f(x,y)0.若f(x,y)x00y00若f(x,y)f(x,y)0.[Ｄ]x00y00F(x,y,)f(x,y)(x,y)在(x,y,)（x,y000000数.F(x,y,)x,y，f(x,y)(x,y)000则0F(x,y,)0f(x,y)(x,y)0x00，即x000x00.F(x,y,)0f(x,y)y0(x,y)0y00000y000f(x,y)(x,y)f(x,y)(x,y)0,x00y00y00x001f(x,y)f(x,y)(x,y)(x,y)0x00y00x00y(x,y)0y0若f(x,y)0f(x,y)0.x00y00,,,n为mAn12s若,,,A,A,,A.12s12s若,,,A,A,,A.12s12sword格式--感谢下载支持若,,,A,A,,A.12s12s若,,,A,A,,A.12s12s[C].(A,A,,A)AB.(,,,)记B12s12s,,,r(B)sr(AB)r(B)sA,A,,A212s1s(1CA为3A21BB12110P010001PC.CC.11PC..［Ｂ］TT.110110110110B010,CB010010A010，001001001001110010C.而P11001,BP(B)0,P(A|B)1P(AB)P()P(AB)P(B)P(AB)P(B)P(AB)P()[B].P(AB)1P(AB)P().P(A|B)P(B)又P(AB)P()P(B)P(AB)P().(XN(,)，YN(,)221122PX1PY1121212[D]1212.1，121121111.2111又(x).1212(x,y)xy1,x02222DDx.DDx1y2y2则1ddy21r12222220Dddy0，22D11故.1xy222222DDD0xx,xsinx(n1,2,)n1nword格式--感谢下载支持limxnn1xx2lim.n1nxnn..x0xsinx10.121xsinx1,n1,2,x0.n1nnxx1xxxnxxn1xn1xxnnnnlimx.nnlxsinxnlsinll0limx0设limxn.1nnnnn11xsinxx2nx2n因limlimnn1n1xxnnnx,t0令tnnt11t111sintsintsintt21limt0t2111t21t1，t0ttttt01t1ttt1t3tt1又t0.ttt362t0t0t0sinx11xsinx1x2nx2n故limlimne.n1n6xxnnnxf(x).x2xx2.xxABf(x)，2xx2xx)2x1x21121111A,Bf(x).32x1x3x1x3312word格式--感谢下载支持11xn(x,x(,x(，而，nn1xx21n0n021x111(1)xx(1)x,x(1,1).故f(x)nnnn1n2xx32n322nn0n0n0fu)在)zfxy22zz220.xy22fu)fu)0；uf(1)f(1)1fu).zzzz2222,0xyxy2222.xy）设u22zxzyfu),fu)y.xxyxy2222x2xy22zxxxy222fu)fu)fu)x2xy2x2y2xy222x2y2fu)fu)，xyxy223222z2y2x2fu).xyy2xy223222zzzz2222将,0得xyxy2222fu)fu)0.uppu）令fu)pp0upuCClnplnulnCp1fu)1.1uuword格式--感谢下载支持1由f1C1fu)u1f(u)lnuC，2由f(1)0C0fu)lnu.2内，函数(,y)|y0f(x,y)具有连t0都有设在上面Df(tx,ty)tf(x,y).DL2yf(x,y)dxxf(x,y)dy0.LQP.xytf(x,y)f(tx,ty)t2x,ty),ty)tf(x,y).3y令t1xf(x,y)yf(x,y)2f(x,y).①xy(x,y),Q(x,y)(x,y)设P(x,y)QPf(x,y)(x,yf(x,y)(x,y).xyxyQP.xyDLyf(x,y)dxxf(x,y)dy0.L9xxxx112343x5xx14x1234axx3xbx11234有3.2ArA；a,bA数a,b.word格式--感谢下载支持的3）设,,12311111A4351,1.a13b1)0,()0A(.1213,,线,则Ax01213123.nr()24r()2r()2.1110r()2.2A432r()）.11111111111111501A4351015.a13b01a3aba0042ab4a52又r()42a0a2.4a50b3bA1111110242A4351101153，2133100000.x2x4x2.134xx5x3234选x,x43x2x4x2134xx5x3.234xx33xx44word格式--感谢下载支持242153xkk，k,k.001121201091,2,1,0,1,1设3ATT12Ax0()求A.)Q,QAQTA3A0AxA0将A的Q.()A131A1331，1313A(1,1,1)T3k0,A0A0,A0,A且012112212kA,0k，121122k,k12)A与,,1212取，1112013,120.21,1622111112,,12word格式--感谢下载支持11136212,,0，122132631111236,,QQ令QA1T1233QT0.09X1,1x021fx,0x2，X4其他0,X,Fx,y(X,Y)令Y.2()求YfyY1,4)F.2.PYy)P(Xy)YF(y)F(y)2YY0F(y)0；当yYy1F(y)P(Xy)PyX当0y2Y113y40dxydx.24y0当1y4F(y)P(Xy)P1Xy2Y1114120dxydxy.24104，F(y)1.当yYword格式--感谢下载支持3,0y18y1f(y)F(y),1y4.YY8y0,其他111,4PX,Y4PX,X4）F2