医科高等数学-习题

1、.医科高等数学医科高等数学习题习题.)2(5:147P22211zxyz11222zyxu改改为为：间断点：间断点：1),(222zyxzyx.)2(21:149Pcos()Dxxy d(0,0) ( ,0)( , ) 其中其中D是顶点分别为是顶点分别为 , 和和 的三的三角形闭区域角形闭区域 32答案是：答案是：.)3(23:149P其中其中D是是由圆周由圆周 及坐标轴所围成及坐标轴所围成的在第一象限内的闭区域；的在第一象限内的闭区域； dyxyxD222211221xyddD2211d22112221121ddtttt11212)28(2:100P.ddxxcos,sin解：令解：令dco

2、ssincosdsin1d2sinsincoscos112d)25(2:100Pdxxx211.coscos11cos1121dccos1cos1ln21coscos112dx1x=sin21xcxx221111ln21.cxx221111ln21cxx2221111ln21cxx211lncxx211lnln.)14(3:101Pdxxx)1ln(2)1ln()1ln(22xxxdxxx解解：原原式式dxxxxxx1122122.dxxxxxxx111222dxxx121) 1(2122xxdcx12cxxxx1)1ln(22原原式式dxxxxxx11122.16:103P求由求由 及其在点

3、及其在点和和 处切线所围成的图形面积处切线所围成的图形面积 243yxx (0, 3)(3,0)xyO3335 . 134 xy62 xy42 xy(0, 3)4 y(3,0)2 y.5 . 102)34()34(dxxxx35 . 12)34()62(dxxxx5 . 102dxx35 . 1296dxxx5 . 13933105 . 131233xxxx49.24:149P计算以计算以xOy面上的圆周面上的圆周围成的闭区域为底围成的闭区域为底, , 而以曲面而以曲面为顶的曲顶柱体的体积为顶的曲顶柱体的体积 22xyax22zxycosaaxyOddVacos02222240cos41ad2

4、244cos4da.2244cos4da2044cos2da 202422cos12da20242cos2cos218da20424cos12cos218da.20424cos12cos218da20424cos2cos2238da0284sin2sin2384a3234a.)4(2:174P221xcey 答案：答案：)7(2:174Pcxxyxy2ln2sin21答答案案：)7(4:174P1 yy)(xPy 令令)2(6:175P)2sin2cos(213xcxceyx答案：答案：.)7(6:175Pxxxy3sin532sin572cos答答案案：.)5(12:61P) 1ln2(8x

5、x答案：答案：xxPx3tantanlim)2(25:632xxxL3sec3seclim222xxxxxLsincos63sin3cos6lim2xxxcos3coslim2xxxLsin3sin3lim23.)0()1 (lim)4(25:63axaPxx)1ln(limxaxxexxaxe1)1ln(lim221)(11limxxaxaLxexaaxe1limae.极值极值求求2024228)()4(27:63234xxxxxfP02444244)(23xxxxf0611623xxx是方程的解是方程的解经观察知经观察知1x6116123xxxx.650666655115611612222

6、323xxxxxxxxxxxxxx.0611623xxx0)65)(1(2xxx0)3)(2)(1(xxx3, 2, 1321xxx11123)(2 xxxf极极小小值值11) 1 (, 02) 1 ( ff极大值极大值12)2(, 01)2( ff极极小小值值11)3(, 02)3( ff.dxxxxP)1 (arctan)15(2:100tdtdxtxtx2,2令令dttttt)1 (arctan22原式原式dttt)1 (arctan22td t arctanarctan2ct2arctancx2arctan.dxxP2arcsin)15(3:10122arcsinarcsinxxdxx

7、dxxxxxx221arcsin2arcsin)1 (1arcsinarcsin222xdxxxx221arcsin2arcsinxxdxx.221arcsin2arcsinxxdxxxdxxxxxarcsin1arcsin12arcsin222xdxxxx2arcsin12arcsin22cxxxxx2arcsin12arcsin22.232)3(5:101xexP答答案案：dxxPee1ln)20(10:102dxxdxxee111lnlncxxxxxdxxxdxlnlnlnln1ln11lnexxxexxxe22.不存在不存在证明极限证明极限yxyxPyx00lim4:147kkkxxkxxkxyx11lim,0原原式式设设极限不存在极限不存在.偏导数偏导数求求xxyzP)1 ()4(6:147)1ln(xyxez)1ln(xyxexz)1)1(ln(xyxyxy)1ln(xyxeyzxyx12xxyxz)1 ( )1)1(ln(xyxyxy12)1 (xxyx.二二阶阶偏偏导导数数求求22ln)2(9:148yxzP2222221yxxyxxz22yxx22222222222222yxxyyxxyxxz22222yxxyyxz2222222yxyxyz.有一阶连续偏导有一阶连续偏导fxyyxxfzP),()5(12:148的的偏偏导导对对求求yxz,2211xy