历年考研数学一真题及答案(1987-)

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1987-20141987()(5,3,15.)(1)x=_____________,2xyx.(2)lnyxe1yx0y_____________.1x(3)1yt2zt121111xyz_____________.(4)L229,xy2(22)(4)Lxyydxxxdy=_____________.(5)123(1,1,0),(1,0,1),(0,1,1),(2,0,0)_____________.(8)a,b22001lim1sinxxtdtbxxat.(7)(1)fg,(,),(),ufxxyvgxxy,.uvxx(2)AB2,AB=AB301110,014A.B(8)26(9)1yyay,0.a(4,3,12.,,)(1)2()()lim1,()xafxfaxaxa(A)()fx,()0fa(B)()fx(C)()fx(D)()fx(2)()fx0,(),stItftxdx0,0,tsI(A)st(B)stx(C)tx,s(D)s,t(3)0,k21(1)nnknn(A)(B)(C)(D)k(4)AnA||0,aA*AA*||A(A)a(B)1a(C)1na(D)na101112nnnxn.102(81)2(1)4,Ixydydzydzdxyzdxdy113()0zyyfxxy,y.210()fx[0,1],[0,1],x()fx(0,1),()fx1,(0,1),x().fxx8,ab,123423423412340221(3)2321xxxxxxxxaxxbxxxax,,?.(3,2,6.)(1),A,pn,A____________;A____________.(2),13,2,24,4.112,21,____________.2,____________.(3)X2211()e,xxfxX____________,X____________.6,XY,()Xfx1001x,()Yfye0y00yy,2ZXY.1988()(3,5,15)(1)1(3)3nnnxn.(2)2()e,[()]1xfxfxx()0x,()x.(3)2221xyz,333.Ixdydzydzdxzdxdy(4,3,12.)(1)21()lim(1),txxfttx()ft=_____________.(2)()fx310(),xftdtx(7)f=_____________.(3)2,(1,1]()fx22x1001xx,()Fourier1x_____________.(4)4234234[,,,],[,,,],AB234,,,,4,4,1,ABAB=_____________.(5,3,15.,,)(1)()fx01(),2fx0x,()fx0xdy(A)x(B)x(C)x(D)x(2)()yfx240yyy00()0,()0,fxfx()fx0x(A)(B)(C)(D)(3)2222222212:,0,:,0,0,0,xyzRzxyzRxyz(A)124xdvdv(B)124ydvydv(C)124zdvzdv(D)124xyzdvxyzdv(4)1(1)nnnax1x,2x(A)(B)(C)(D)(5)n12,,,(3)ssn(A)12,,,,skkk11220sskkk(B)12,,,s(C)12,,,s(D)12,,,s(6)()(),xyuyfxgyxfg,222.uuxyxxy(8)()yyx322e,xyyy(0,1)21yxx,().yyx9(0,1)AM2(0kkr,rAM),M22yxx(2,0)B(0,0),OAM.6,APBP100100000,210,001211BP5,.AA820000101xA20000001yB.(1)x.y(2)1PAPB.P9()fx[,]ab,(,)ab()0,fx:(,)ab,()yfx(),yfxa1S()yfx(),yfxb2S3.(3,2,6.)(1),A,A19,27A____________.(2)(0,1),65____________.(3)X10,0.02,221()e,(2.5)0.9938,2uxxduX(9.95,10.05)____________.6X21(),(1)Xfxx31YX().Yfy1989()(5,3,15.)(1)(3)2,f0(3)(3)lim2hfhfh=_____________.(2)()fx,10()2(),fxxftdt()fx=_____________.(3)L21,yx22()Lxyds=_____________.(4)divu(1,1,0)Pdivu=_____________.(5)300100140,010,003001AI1(2)AI=_____________.(5,3,15.,,)(1)0x,1sinyxx(A)(B)(C),(D),(2)224zxyP2210,xyz(A)(1,1,2)(B)(1,1,2)(C)(1,1,2)(D)(1,1,2)(3),(A)11223cycyy(B)1122123()cycyccy(C)1122123(1)cycyccy(D)1122123(1)cycyccy(4)2(),01,fxxx1()sin,,nnSxbnxx102()sin,1,2,3,,nbfxnxdxn1()2S(A)12(B)14(C)14(D)12(5)An,A0,AA(A)0(B)(C)(D)(3,5,15)(1)(2)(,),zfxygxxy()ft,(,)guv,2.zxy(2)2()cxydxyxdy,()x,(0)0,(1,1)2(0,0)()xydxyxdy.(3)(),xzdv22zxy221zxy.(6)1()arctan1xfxxx.(7)0()sin()(),xfxxxtftdtf,().fx70ln1cos2exxxdx(0,).6,13xx123422xxx1236423xxx,.8nA,(1)11A.(2)AA*A.9R2222(0)xyzaa,R,?(3,2,6.)(1)A()0.5,PAB()0.6PB(|)0.8,PBAAB()PAB=____________.(2),0.60.5,,____________.(3)(1,6),210xx____________.6XY,X1()2,Y.23ZXY.1990()(5,3,15.)2xt(1)(1,21)M34yt_____________.1zt(2)a,lim()xxxaxa=_____________.(3)()fx1011xx,[()]ffx=_____________.(4)2220eyxdxdy_____________.(5)1234(1,2,3,4),(2,3,4,5),(3,4,5,6),(4,5,6,7),_____________.(5,3,15.,,)(1)()fx,e()(),xxFxftdt()Fx(A)e(e)()xxffx(B)e(e)()xxffx(C)e(e)()xxffx(D)e(e)()xxffx(2)()fx,2()[()],fxfxn2,()fxn()()nfx(A)1![()]nnfx(B)1[()]nnfx(C)2[()]nfx(D)2![()]nnfx(3)a,21sin()1[]nnann(A)(B)(C)(D)a(4)()fx0x,0()(0)0,lim2,1cosxfxfx0x()fx(A)(B),(0)0f(C)(D)(5)12AXb1,2AX01,k2k,AXb()(A)1211212()2kk(B)1211212()2kk(C)1211212()2kk(D)1211212()2kk(3,5,15)(1)120ln(1).(2)xdxx(2)(2,sin),zfxyyx(,)fuv,2.zxy(3)244exyyy().(6)0(21)nnnx,.(8)2SIyzdzdxdxdyS2224xyz0z.7()fx[,]ab,(,)ab,()().fafb(,)ab,()0.f61100213401100213,0011002100010002BCA1()AECBCEE1,CC,CC..A822212312132344448fxxxxxxxxx.8PAB,(1,2)A(3,4)BF().FPO,OPy.2FP.(3,2,6.)(1)X1()e,2xfxxX()Fx=____________.(2)AB0.40.30.6,BB,AB()PAB=____________.(3)X2()Poisson,22e{},0,1,2,,!kPXkkk32ZX()EZ=____________.6(,)XY:01,Dxyx,X21ZX().DZ1991()(5,3,15.)(1)21cosxtyt,22dydx=_____________.(2)2222xyzxyz(,)zzxy(1,0,1)dz=_____________.(3)1212321:;:.101211xyzxyzll1l2l_____________.(4)0x123,(1)1axcos1x,a=_____________.(5)452002100,00120011AA1A=_____________.(5,3,15.,,)(1)221e1exxy(A)(B)(C)(D)(2)()fx20()()ln2,2tfxfdt()fx(A)eln2x(B)2eln2x(C)eln2x(D)2eln2x(3)12111(1)2,5,nnnnnaa1nna(A)3(B)7(C)8(D)9(4)Dxoy(1,1)(1,1)(1,1)1,DD,(cossin)Dxyxydxdy(A)12cossinDxydxdy(B)12Dxydxdy(C)14(cossin)Dxyxydxdy(D)0(5)nABC,ABCEEn,(A)ACBE(B)CBAE(C)BACE(D)BCAE(3,5,15)(1)20lim(cos).xx(2)n222236xyz(1,1,1)P,2268xyuzPn.(3)22(),xyzdv220yzxz4z.(6)(0,0)O(,0)Asin(0)yaxa,,LOA3(1)(2)Lydxxydy.(8)()2(11)fxxx2,211nn.7()fx[0,1],(0,1),1233()(0),fxdxf(0,1),c()0.fc81234(1,0,2,3),(1,1,3,5),(1,1,2,1),(1,2,4,8)aa(1,1,3,5).b(1)ab,1234,,,?(2)ab,1234,,,?.6An,En,AE1.8,(,)PxyPQ(Qx),(1,1)x.(2,3,6.)(1)X22,{24}0.3,PX{0}PX=____________.(2)202(yaxxa),,x4____________.6(,)XY(,)fxy(2)2e0,00xyxy2ZXY.1992()(5,3,15.)(1)()yyxecos()0xyxy,dydx=_____________.(2)222ln()uxyz(1,2,2)MgradMu=_____________.(3)()fx211x00xx,2x_____________.(4)tancosyyxxy=_____________.(5)111212121212,nnnnnnabababababababababA0,0,(1,2,,).iiabinA()rA=_____________.(5,3,15.,,)(1)1x,1211e1xxx(A)2(B)0(C)(D)(2)1(1)(1cos)(nnan0)a(A)(B)(C)(D)a(3)23,,xtytzt,24xyz(A)1(B)2(C)3(D)(4)32()3,fxxxx()(0)nfn(A)0(B)1(C)2(D)3(5)12100,121AX0,A(A)212(B)201011(C)102011(D)011422011(3,5,15)(1)20esin1lim.11xxxx(2)22(es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