高等数学试题库完整

经典word整理文档，仅参考，双击此处可删除页眉页脚。本资料属于网络整理，如有侵权，请联系删除，谢谢！入学考试题库（共180题）1．函数、极限和连续（8xxlgarcsin1yAx23[[；；[(1,3]；[.11(x)[2,]f()2f；则D3x11[,3][,0)[3,)；2211[,0)(0,3](,][3,)；.22(x)的定义域是[xB(log)ff21111[,0)(0,4][,4][,0)(0,2][,2]；；；.4422(x)的定义域是[xD(log)4ff31111[,0)(0,3][,3][,0)(0,9][,9].；；；C3399(x)f(arcsinx)5f1[0,1]；[0,]；[0,]；[0,].222x21x21,xf(x)设fx2()Ax2x1x12x1x1x1x12x1.．；；；x13x7yy（B31xlog1x)xxxlog()log()log()．；；；.1x1xx1x3333x2x)1x2()8ffx()C2x1x21x21x2．；；；.2x12x12x12x12222lim(123nn)9()Bn2n113.1；；；2123nlim(A2n2n114151；．；；45111limC(1223n(n1)n；；；.1111(1)n2222nlim(A111132nn449994．；；；94xx2(Cxx11；；1.1．；22x11(Axx011222．；；；.23x11（Bxx032321212；；；.2x11x1（Cx1；0；1；2.2x13lim(Bx2x44343334．；；；.4x1x22()Dx．；；；x5x62()Dx2x2．；；；x13(Ax5x32x273711．；；；)C.333x12(x5x42x23234．；；；.3sinxlim(Bxx1012．；；；.1limxsin(Bxx01012．；；；.sintxdtt1lim(B0x2x0112113．；；；.23x2xk24k（Ax3x311.33．；；；33x2x32(B3x13x．；；；0ln(12)xxAx与2D1．x0x0xx1x.1．Dx20x0x2.xxx20kx2与kx（C311211．；；；.2331limxsin（Cxx10122．；；；..sin2xlim（Dxx0101．；；；sin3xlim（A4xx03443；；；.sin2xsin3xlim（C；Cx0332323．；；.22tanxlim（xx01012．；；；.lim1cosx（Ax2x011131.．；；；223(1lim(1)elim(1)；xe；xxxx0x011lim(1x)elim(1)e；B.xxxxx1lim(1)2（xxx．e2；e2；e；e1.1lim(1)（Dx3xx11．e3；e3；e；e.33x1x1lim()（Axx．e2；e2；e；e1.x2lim()（Dxx2xe4；e2；；e4.5lim(1)（Bxxx11．e5；e5；e；e.551lim(13x)（Axx011．e3；e3；e；e.33xlim()（5Ax1xx．e5；e5；；1.ee2x)lim（Dxx01012．；；；.8sin3(x1)x1,x1x1(x)fk=(4xk,1．sin(x1),x1(x)1fxk=(arcsinxk,x122．x．22x1(x)2fk=(ek,x1x1．xx12(x)fk=(xk,x11x3．1ex,x02(x)fk=(x)k,x03x6．7677676．sinax2,x0x0x(x)1,x0af在b(x)bx,0x01；0；；0．x2,x0(x)x0fDx2,x0.xlnx,x0f(x)01,x0xB.f(x)yf(x)（yxxB00.yf(x)（f(x)yxxC00.f(x2x)f(x)lim1f(x)（A00x0x011222．；；；.2f3x)f2（Bf3xx0；；2；3.f(2x)f(2x)(2)3lim（fDxx0；；3；6.f(2x)f(0)f(x)在x0f(0)2lim（Cxx0；；；．f(6)f(6x)5x(6)10lim（fx0２；２；；.f(3x)f(3)(3)6lim（f2xx0；；3；6.xx111Cy32xy102xy102xy102xy10；；；.11(2,)4yAx21111xyxyy；；；44144111xyx.441441(3,)3yBx12123xyxyy；；939123123xyx；.99xx2y4x1My2C3773；；(,)；(,).2442xsinxyy=(1cosxxsinx1cosxsinxx1cosxsinxx1cosxsinxx1cosx；；；.lnxyy=(xxxxx；；；；.lnsinxy=(yxxx；；.arctan1x1xyy=(1111y；；；.1x21x21x21x2sin(3x2)y=(cos(3x)cos(3x)6xcos(3x)6xcos(3x)2；2；2；2.d71f(lnx)xf(x)(dxx2；x2；e2x；e2.xeeyxy=(yxexexeyeyyyxx；；；.eyxeyxxexyeyyarctanlnxyy22=(xxyxyxyxyyxyxyx；；；.yxy=(Bxx)xsinxxsinx)1xxx[cosln()xx]；x；1xxx)1xsinxxsinxx1xsinx[ln()][cosxln()]；.1xxx)1x1x1x1xy=(1111；；；.1x21x21x21x2f(x)yxC0f(x)yf(x)yxx00limf(x)f(x)；yf(x)x.00x0f(x)77yxA0limf(x)yf(x)x.0x0f(x)yf(x)yxx00ln(sinx)y=(22tanxdxtanxdx2cotxdxcotxdx.；；；lny50xe=(yyy1yy；；；.111yyyyxy=(Ax(lnxdxx(lnxdx；xx；x(lnx(lnx.；ln(x)2tanxlim(x21；；；．x3(xxx06；；；．1limx(1e)(xx；；；．．11lim()(sinxxx0；；；limx(sinxx00；；；．limx(tanxx01；；；e1．1tanxlim(xx0．0；；；e1．x6x4y32((,0][4,)和(,0)(4,)和；．；(0,4)．；x3x1y32((,0)(4,)．．．(,1]；；；；((,0][1,)[0,)．；；xey2(x1211212e1；在xxe1；21ex1e2．在x2；在(x)x9x15x3f32(x5；110x110x5；在x在x在x1x51x510；10．(x)2xf(x)(f112；x2；x；.x2xx2x222(x)sinxf(x)(f，则xxcosxcosx；；；.cosxf(x)f(x)是(sinxsinxsinxCsinxC.；；；((x)dx2arctan(2x)cf(x)f1248；；；.14x214x214x214x2xsindx2(21111xsinxCxsinxC；2222121121xsinxCxsinxC.22cos2xdx(cosxsinxsinxcosxCsinxcosxCsinxcosxC；sinxcosxCcos2xdx.(sinxcosx22cotxtanxCcotxtanxCcotxtanxCcotxtanxC；.tanxdx2(tanxxCtanxxC；tanxxC(x)f(x)tanxxC.f(e)edxF是(xx(e)CF(e)CF(e)CF(e)C．Fx．．．xxx)fx(，x11cxccxc.xx)fx(x)e(f，xx11cxccxc.xxf(2lnx)(x)edxfx(2x11cc4xcxc2.24x2x2fx)(x)sinx(f，1x2cxcsinxccosxc.x2sin3xdx(1313cos3xCcos3xCcos3xCcos3xC.311e(xx2111111CeCeCeCe.xxxxxxtanxdx(xCxCxCxC.dx(x2(x2)C(x2)C；2；2x2Cx2C.；1dx(1cosxcotxcscxCcotxcscxC；；cotxcscxCcotxcscxC；.1dx=(1cosxcotxcscxCcotxcscxC；；cotxcscxCcotxcscxC；.1dx1sinxtanxsecxC(tanxsecxC；；tanxsecxCsinxtanxsecxC.；dx(1sinxsecxxxcsecxxxcsecxxxc；；；secxxxc.1dx1sinxtanxsecxC(tanxsecxC；；tanxsecxCtanxsecxC.；dx(xlnxxCxC；；lnxCxlnxC2；1.1(xx)xarctanxC；xarctanxC；arctanxC2arctanxC；.ex(1exln(e1)Cln(e1)C；；xxln(e1)Cxln(e1)C.x；xxcosxdx2(1111xsin2xC；xsin2xC；21412141sin2xCxsin2xC.x；2424cosxdx3(11sinxsinxCsinxsinxC3；；3；3131sinxsinxCsinxsinxC33.33x1(x2(x1arctan2(x1arctanx1)C；2(x1arctanx1)C；x1)C；2(x1arctanx1)C.sinxxfxdx(x)是f(xsinxsinxcosxcosxCcosxcosxC；；xx2sinx2sinxCC；.xxarccosxf(x)是xf(x)dx（Bxxxcxcxc；；1x21x2xxxc；.1x21x2arcsinxf(x)是(x)dx(xxxcxc；；；1x21x2xxxcxc.1x21x2xf(x)是(x)dx(xxarctanxcarctanxcarcsinxc.；；1x2x1x2xarctanxc；1x21x2fe)xx(x)lndx(f，3exxCxC；；；11CxCx.33xedx(xeeCxeeC；；；xxxxeCeC.xxxx1(xx)2211x1xarctanxCarctanxCarctanxC；；；x1arctanxC.xx4(1x211xarctanxCxxarctanxC；x；；3333131xarctanxCxxarctanxC3x.331dx(x2x52x11x1arctanCarctanC；；；2221arctan(x1)Carctan(x1)C.21dx(x2x321x11x3CCC；；；4x34x11x31x1C.4x14x3t)xfCa()()fxfx(x)f(x)f.(x)sin(2t)x()x(0cos(2x)x)sin(2x)2sin(2x).(x)1tdt()(x2x01x1x1x1x.2x2x(x)()FxxF（Basintsinxcost；cosx.；；xt)lnxf(x)(f0xsecxxcscx2222.ft)xx()fxx3(0sinx6xsinx6xx3x2x3x2.11(dxx22ln2ln3ln3；.；C1111xx．()xx()．x．x．21111(x)[a,a]在fxfx[()(（afAa0；1；2；C3.1111xx．()xx()．x．x．21111(x)[a,a]在fxfx[()((afa2f(a)2f(aa213(dx1x21.126312x(0-2；；；19(xx12ln22；；.13dx(eexx0；；.3461211(dxx)023222；.2；22kk(1x2011411.3562(x0131151.46xy122arcsinz(4ln(xy)22{(,y)1xy{(,y)xy；2222{(,y)1xy{(,y)xy2222.y(xy,)(xy)xf(x,y)(fxyy2xx2.1x21x1y21y(xy,xy)xyf(x,y)f2(22yx2y2y2x2y2x2x.2z2lnxy（z22y22yxxy2222；；；.(xy)(xy)(xy)(xy)222222222222yxz2arctan(zy22(xy)yxxy2222；；；.(xy)(xy)(xy)222222222222yy,yxf(x,y)xfx2(2x2x(y1y2x(y1y2y(x1)2y(x1)1x；；；.1xz2x（zyAy(1ylnx)(1xlny)xx(1ylnx)；x；y1y1x(1xlny)y1x；.y1zdz(yxyxy；；xy2xy2xy2xy22222yxyx；.xy2xy2xy2xy22222yarctanxdzz(xyxy；；xy22xy2xy2xy2222yxyx；.xy2xy2xy2xy22222ln(2xy)zdz(22xx2；；xy2xy2xy2xy222yy2；.2xy22xy2xy2xy2xdz(zyyxdyyxdxxlnxdy；xlnxdx；yy1y1ydxxdy；xdxyxdy.yxy1yyy1ydz（zAxxydxylnydy；ylnydxxydy；x1xxx1xlnxdyxlnxdxyxdyyxy1dx；.yyy1yzez(xxyxyyxyxyearc