《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函数极限和连续题）8）xxlgarcsiny（Ax23[(2,3][3,3]；；[3,0)(1,3]；[2,0)(1,2).11(x)f的定义域是[2,]()则f（D3x11[,3][,0)[3,)；；2211[,0)(0,3](,][3,)；.22(x)的定义域是[f则(log)x（Bf21111[,0)(0,4][,4]；[,0)(0,2][,2].；；4422(x)的定义域是[f则(log)x（Df31111[,0)(0,3][,3]；[,0)(0,9][,9].；；3399(x)f(arcsinx)（Cf则1[0,1]；[0,[0,]；[0,].]；222x21x21f(x),设2则()Afxxx2x1x12x1x1x1x1．；；；.2x12x13xy（By31x.学习帮手.......xxx1x．log()；log()；log()；log().1x1xx1x3333x2)()则fx(fx)C2x1x21x21x21x2．；；；.2x12x12x12x12222）123nnlim()()Bn2n11；；；.23123nlim()A2n2n1141515．；；；4111lim()C1223n(n1)n；；；.1111(1)n222111322nlim()A1nn44999．；；；944x2x()Cxx112．；11.；；2x11()Axx0.学习帮手.......112．；22.；；23x11（Bxx03321212；.；；22x11x1（Cx1；0；1；2.2x13lim()Bx2x44343334．；.；；4x21x2()Dx．；；；x25x6x2()Dx2．；；；x31()Ax25x3x273711．；；；.333x12()Cx5x42x23234．；；)B；.3sinxlim(xx1012．；；；.1limsinx()Bxx01012．；；；..学习帮手.......sintt1xdtlim()B0x2x01121313．；；；.2x2xk2若4则k（Ax3x31313．3；；3.；x2x32()B3x13x．；；；0当x，ln(122)x与x（D2；；；（A。1．．x0x0；xx；1；x100.101（Dx20x0x2x；；x2；x.x0时若2与当，则k（Ckx311211．；；；.233.学习帮手.......1limsinx（Cxx1012．；；；.limsin2x（Dxx01012．；；；.sin3xlim（A4xx034；；；.43sin2xsin3xlim（Cx0332223．；；；.23tanxlim（Cxx01012．；；；.lim1cosx（Ax2x01111．；；.；2233(1lim(1)lim(1)xe；e；xe；e.xxx0x011lim(1)lim(1)xxxxxx1lim(1)2x（Bxx．e2；e；e；.e121lim(1)（Dx3xx11．e3；e；.33e；e3.学习帮手.......x1x1lim()（Axx．；e；.e1e；e22x2lim()（Dxx2x；；；e2e4e.45lim(1)（Bxxx11．e5；.e；e；e5551lim(13)x（Axx011．；3.e；e3e；e33xlim()（A5x1xx．e5；.e；e；e512x)lim（Dxx01012．；；；.8）sin3(x1)x1,x1x1()fx则k=(xk,．sin(x1),x1()1fxx则k=(arcsinxk,x122．．22xx1()2fx则k=(ek,x11x.学习帮手.......．xx12()fx则k=(xk,x11x．1ex,x02()fx则k=(x)k,x03x66767．．776sinax2,x00x()1,在x0ab(fxxx)bx,0x；；；．x2,x00f(x)是（D设()则xfx2,x0x；；；.xlnx,x00f(x)是（B设()fx则x1,x0；；；.一元函数微分学））yf(x)()xxyfx（B00.学习帮手.......；；；.yf(x)()xxyfx（C00；；；.f(x2x)f(x)()若lim1则fx（A00x0x0112．；2.；2；2f3x)f2则（f(2)B3xx0；；2；3.f(2x)f(2x)(2)3lim（f则Dxx0；；3；6.f(2x)f(0)(x)x0在f(0)2f且则lim（Cxx0；；；．f(6)f(6x)(6)10lim则f（5xx0２；２；；.f(3x)f(3)(3)6limf则（2xx0；；3；6.1yx（C3x2xy102xy102xy102xy10；；；.11(2,)（Ayx24.学习帮手.......1111x；yx；y41414141yx；yx.4141441(3,)3y（Bx2123xyx；y；9391923192x.yx；y32x41yxxMy2（C3773(1,0)；(0,1)；(,)；(,).2442xsinx则y=(y1cosxxsinxsinxxsinxxsinxx；；；.1cosx1cosxy则=(1cosx1cosxlnxyxxxx.y；；；；lnsinxyx则=(xxx.；；1xarctan则y=(y1x1111；；；.1x21x21x21x2sin(3)2x则y=(ycos(3)x；cos(3)6cos(3)x.6cos(3)x；xx；x2222d(ln)()fxx则fx(dx；；e2xx2x；2e.2xxyee则y=(yx.学习帮手.......exexeyeyyyxx；；；.eyxeyxxexyeyyarctanlnxy则y=(22xxyxyxyyxyxyx；；；.xyyx则y=(Bxx)；x1xxx)xsinxxsinx[cosxln()]；1xxx)1xxsinxxsinxx1xsinx[ln()]；[cosln()].x1xxx)1x1x1x1x则y=(1111；；；.1x21x21x21x2yf(x)x（0Cyf(x)()()x；yfxx；00lim()()fxfx；yfxx.00x0yf(x)x（0Alim()fx.()yfxx；0x0yf(x)()yfxx．x；00ln(sin)yx则=(22tanxdxtanxdx2cotxdxcotxdx；.；；ln50xey则=(y.学习帮手.......yyyy；；；.1111yyyyyx则=(Ax(ln1)(ln1)dx；xxxdx；xxx(lnx(lnx.；）ln(x)2lim(tanxx2；；；．x3(xxx0；；；．1lim(1)xe(xx；；；．．11lim()(sinxxx0；；；limxsinx(x0e；；；．limxtanx(x0e；；；．e11tanxlim(xx0.学习帮手.......．；；e；．e164yx3x2((,0][4,)和(,0)(4,)和；．；(0,4)[0,4]；．31yx3x2(．(,0)．(,1]；；(4,)；[0,2]；．((,0])[0,)；．；yxe2(x121e1121在；在；e1xx22在x1；在x1．e2e2()9153fxx3x2x(110x5在x在；1在x5；10在x在x在x1在x51在x5；1010．一元函数积分学））(x)2xf(x)(f则.学习帮手.......112x.xx；xx；x；222222(x)sinx，则f(x)f(xxcosx；x.；；cosxf(x)是f(x)(I则sinxsinxsinxCsinxC.；；；((x)dx2arctan(2x)cf(x)f则1248；；；.14x214x214x214x2xsin2(dx21111sinsinxxCxxC；222211121sinsinxxCxxC.222cos2x(dxcosxsinxsinxcosxCsinxcosxCsinxcosxC；sinxcosxCcos2x.dx(sinxcosx22cotxtanxCcotxtanxCcotxtanxCcotxtanxC；.tan(xdx2tanxxCtanxxCtanxxCtanxxC；.(x)f(x)是()feedxF．则(xx()Fe()C．FeC．Fe()()C．FeCxxxx.学习帮手.......)fx，(x11xc..cxccxx1)fx()(fxe，xx1xccxccxxf(2lnx)()dx(fxe则x2x114c.ccxcx(224x2x2fx)(x)sinxf，1x2xcxcxcsincosxc.2sin3xdx(113cos3xCcos3xCcos3xC.cos3xC3311e(xx2111111xeCeCxeCxeC.xxxtanxdx(xCxCxCxC.dx(x2(2)(2)xC；xC；22x2Cx2C.；1(dx1cosxcotxcscxCcotxcscxC；；cotxcscxCcotxcscxC；..学习帮手.......1=(dx1cosxcotxcscxCcotxcscxC；；cotxcscxCcotxcscxC；.1dx(1sinxtanxsecxCtanxsecxC；；tanxsecxCsinxdxtanxsecxC.；(1sinxxxxcxxxc；；；xxxcxxxc.1dx(1sinxtanxsecxCtanxsecxC；；tanxsecxCtanxsecxC；.dx(xlnxxCxC；；lnlnxC；xxC.211(xx)xarctanxC；xarctanxC；2arctanxCarctanxC.；ex(1exln(ex1)xC；ln(e1)C；ln(1)ln(1)xexC；xeC.x.学习帮手.......cos(xdx21111xsin2xC；xsin2xC；21412411xsin2xC；sin2xxC.2424cos(xdx311sinsinsinsinxxC；xxC；333131sinsinsinsinxxC；xxC.3333x1(x2(x1arctanx1)C；2(x1arctanx1)C；2(x1arctanx1)C2(x1arctanx1)C；.sinxxfxdx()(是fx则xsinxsinxcosCcosxC；x；；xx2sinx2sinxcosCcosxC.xxxarccosxf(x)是xf(x)dx则（Bxxxc；xc；1x21x2xxxc；xc.1x21x2arcsinxf(x)是则()xdx(xxxc；xc；1x21x2.学习帮手.......xxxc；xc.1x21x2xf(x)是则()xdx(x1x2xxxcarctan；xcarctan；1x2xxcarctan；xcarcsin.1x21x2xfe)()lnx(fx，dx3exxC3xC；；11xC；xC.33(xedxxeC；eC；xxxxeC；eC.xxxx1(xx)2211x1xarctanxC；arctanxC；x1arctanxC.arctanxC；xx4(1x211arctanarctanxx3xC；xxxC；331331xxarctan3xC；xxarctanxC.331dx(x2x52.学习帮手.......x112x1arctanarctanC；C；221arctan(x1)C；arctan(1)xC.21dx(x22x31x11x3；；CCC4x34x11x31x1；C.4x14x3）x()ft（Ca()()fx；fx；(x)f(x)f；.(x)()t)则(xx0cos(2x)x)sin(2x)2sin(2x).()1则(x)(xxtdt201x1x1x1x.2x2x()()则Fx（设xBFxasintsinxcostcosx.；；；xft()()ln则fx(x0secseccscxxxx.2222()()3则fx(xxxft0sinx6xsinx6x3xxxx.322.学习帮手.......11(dxx22ln2ln3ln3；；.（CB．111A．．1()x2xC．xx()111xx1(x)[a,a]在[()fxfx(若f则a（Aa0；1；2；3.（CB．111A．x2xC．xx()111．1()xx1(x)[a,a]在[()fxfx(f则a(a2f(a)2f(aa213(dx1x21(.126312x0；；；19(xx12ln22；；.13(dxeexx0；；.34612.学习帮手.......11dx(x)0232222；；.22k则k(1x20114151.362x(011151.346多元函数微分学））xy122arcsinz(4ln(xy)22,)1xyxy,)；xyxy2222,)1xyxy,).xyxy2222y(fxy,)()(,)xyx则fxy(xyy2xx2.1x2111yxy2(,)(,)fxyxyxy则fxy(222yx22yy22xy22x.x2z2lnxy则（z22y.学习帮手.......22yxxy2222；；；.(xy)(xy)(xy)(xy)222222222222yxz2arctan设(z则y2(xy)2(xy)yxxy2222；；；.(xy)(xy)222222222222f(x,y)y设,则(fxyyx22xx2x(y1y2x(y1y2y(x1)2y(x1)；；；.1x1xz2zxy则（Ayyx；(1ln)yx；(1ln)xxxxy1y1y1y1xy；(1ln)xy.(1ln)xyz则dz(xyxy；；xy2xy2xy2xy22222yxy2xyx；.xy2xy2xy22222yarctanz则dz(xxyxy；；；xy2xy2xy2xy22222yxy2xyx.xy2xy2xy22222ln(2)zxy则dz(22xxy2x2；；xy2xy2xy2.学习帮手.......22yy2；.2xy22xy2xy2xy2zxy则dz(lnxdxyxdy；lnyxdxxxxdy；yy1y1yyxdxxdy；xdxyxdy.y1yyy1zy则dz（Axlnxydxylnlnydxxydy；ydy；yxdy；xx1xxyx1yxdxxy1lnxdxyxdy.yy1yzezx则(xyxyyyyearctanyearctanxearctanxearctanxxx；；；.x