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极限、导数、积分基础计算题一、计算下列极限(1)112lim221xxxx(2)121lim22xxxx(3)4586lim224xxxxx(4))2141211(limnn(5)35)3)(2)(1(limnnnnn(6)xxx10)1(lim(7)xxxx2)1(lim(8)xxxx30sinsintanlim(9)xxe10lim(10)2)11(limxxx(11)21)63(limxxxx(12)exxex1lnlim(13)221)1(1limxxxx(14)1)1232(limxxxx(15))0,0,0()3(lim10cbacbaxxxxx(16)xxxtan2)(sinlim(18)xxx2321(19)1lim22x43xxxx(20))lim(11)(21x2xx(21)2(n1)32lim1nn(22))3lim(1x1x3x11(23)xx10lim(12x)(24)xxlim(11)(25)1sinx1)1)(1(lim30x2kx(k为常数)sinxtanxx(26)xxlimlnsin0(27)xx2x)cot20lim(13tan(28)xxxxxx1sin201sinlim1tan(29)(1x)(1x)11lim320exexe3xxx21x)(30)limx(x(31)limtanxsinx0x3x(32)(a0)limlnxaxlnaxax32x2xlim4x(33)11tanlim20xxxx(34)xeexxxsinlim0(35)xxx5tan3sinlim(36)2120limxxex(37)xxxa)1(lim(38)xxxtan0)1(lim.(39)xxlimln(1x)0(40)xxxxxsinlimtan0(41)x(2x)22limlnsinx(42))11lim(221xx1x(43)xxxsin0lim二、求下列函数的导数(1)xylnx(2)yx2lnxcosx(3)y(2x5)4(4)ye3x2(5)ysin2x(6)xx1ln1lny(14)ln32exyx(15)tts1cos1sin(16)ycos(43x)(17)yln(1x2)a2x2(18)y(19)xysin2xa2x2)(20)yln(x(21)(22)2yln(cscxcotx)ylntanx1ln2x(10)y(23)yearctanx(11)ysinnxcosnx(24)1arctanx1yx(12)xyxarccosarcsin(25)ylnlnlnx(13)xxyxx1111(26)xxy11arcsinx(7)yarcsin(8)(9)yln(secxtanx)y(arcsinx)22(27))32(2xxeyx(33))sin(sin22xxy(28)2)2(arctanxy(34)nxxyln(29)xey1sin2xx(35)y(30)242arcsinxxxy(36)212arcsintty(31)yarcsin(sinx)(37)xxy11arctan(32)xxxytanlncos2tanln(38))1ln(2xxeey(39)yxx(x0)三、求下列函数的二阶导数(1)y2x2lnx(2)yxcosxa2x2(3)y(4)ytanx(5)y(1x2)arctanx(6)yxex2(7)ycos2xlnx(8)ye2x1(9)yetsint(10)yln(1x2)(11)1y13x(12)xyex1x2)(13)yln(x(14)1x2xy四、求下列参数方程所确定的函数的导数dxyd,22ddxy(1)y32btxat(2)1cossin)(yx(3)y33sincosaxa(4)yttxarctan1ln2五、求由下列方程所确定的隐函数的导数dxyd(1)y22xy90(2)xyexy(3)x3y33axy0(4)y1xey22ddxy六、求由下列方程所确定的隐函数的二阶导数(1)x2y21(2)ytan(xy)七、求下列不定积分(1)2dxx(2)xxd(3)xxx2d(4)5x3dx(5))(2d是常数gghhxxxd)1)(13(7)xxexd)32((8)xxeexxd)1((9)xxxxd32532(10)xxd2cos2(11)xxxxdsincos2cos(12)cot2xdx(3)b2x2a2y2a2b2(4)y1xey(6)(xdx(13)x(14)x23xdx(15)xndxm(16)(17)(x23x2)dxx21)2dx((18)xxx)2d(1(19)xx)d121(3x22(20)3xexdx(21)secx(secxtanx)dxxx1cos2dxcos2xsinxx2dcos2(24)cos(tansec)d(25)xx4xx2d1232(26)(32x)3dxxxxd122(28)e5tdt(22)(23)(27)(29)xx21d(30)xeaxbxd)(sin(31)xxexd2(32)xxxd322(33)xxxxd5212(34)xxxdcossin3(35)tan10xsec2xdx(36)221)(arcsindxxx(37)221d1tanxxxx(38)xxxxd)ln(ln12(39)xxxxdcossintanln(40)ttd)(cos2(41)2cosxcosxdx(42)xxxdsectan3(43)xxxd4912(59)12d2xx(45)xsinxdx(46)arcsinxdx(47)323dxx(48)tttdsin(49)xcos(x2)dx(50)xxx4d13(51)cos2(t)sin(t)dt(52)xxxxdsincos3sinxcos(42)xxxlnxlnlnd(54)xxxd11022arccos(55)xxxd(1x)arctanxxsinxcosd(57)cos3xdx(58)sin2xcos3xdx(59)sin5xsin7xdx(60)exexdx(61)xxxd239(62)(x1)(x2)dx(63)lnxdx(64)xexdx(56)(65)x2lnxdx(66)xxexd2sin2(67)x2arctanxdx(68)x2cosxdx(69)ln2xdxxx(70)xd2cos22(71)xxxd2sin)1(2(72)xexd3(73)(arcsinx)2dx(74)xxxxd5212(75)xxd133(76))3)(2)(1(dxxxxx(103)))(1(d22xxxx(105))1)(1(d22xxxx(79)xxxxd)1(2222(80)excosxdxxdx(81)x2cos(82)xtan2xdx(83)te2tdt(84)xsinxcosxdx(85)xln(x1)dxxxlnxd23(87)coslnxdx(88)exsin2xdx1)dx(x2x(90)xxd(x1)(x1)122(91)xxxxx8d345(92)xd11x4(93)xd(x21)(x1)22(94)3sin2xxd(89)(86)
本文标题:考研数学-215道基础计算题
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