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1微积分初步形成性考核作业一、填空题(每小题2分,共20分)1.函数)2ln(1)(xxf的定义域是),3()3,2(2.函数xxf51)(的定义域是)5,(3.函数24)2ln(1)(xxxf的定义域是]2,1()1,2(4.函数72)1(2xxxf,则)(xf62x5.函数0e02)(2xxxxfx,则)0(f2.6.函数xxxf2)1(2,则)(xf12x7.函数1322xxxy的间断点是1x8.xxx1sinlim1。9.若2sin4sinlim0kxxx,则k210.若23sinlim0kxxx,则23k1.曲线1)(xxf在)2,1(点的斜率是21)1(fk2.曲线xxfe)(在)1,0(点的切线方程是1xy3.曲线21xy在点)1,1(处的切线方程是)1(211xy即:032yx4.)2(xxxxx22ln22ln2125.若y=x(x–1)(x–2)(x–3),则y(0)=-66.已知xxxf3)(3,则)3(f3ln27277.已知xxfln)(,则21)(xxf8.若xxxfe)(,则)0(f29.函数yx312()的单调增加区间是),1[10.函数1)(2axxf在区间),0(内单调增加,则a应满足0a1.若)(xf的一个原函数为2lnx,则)(xf2ln2xxxc2.若)(xf的一个原函数为xx2e,则)(xf24xe3.若cxxxfxed)(,则)(xf1xxe4.若cxxxf2sind)(,则)(xf=2cos2x5.若cxxxxflnd)(,则)(xf1x6.若cxxxf2cosd)(,则)(xf4cos2x7.xxded22xedx8.xxd)(sinsinxc9.若cxFxxf)(d)(,则xxfd)32(1232Fxc10.若cxFxxf)(d)(,则xxxfd)1(22112Fxc1.32d)2cos(sin112xxxx2.xxxxd)cos4(22523.已知曲线)(xfy在任意点x处切线的斜率为x,且曲线过)5,4(,则该曲线的方程是313223xy4.若dxxx)235(1134.5.由定积分的几何意义知,xxaad022241a6.e12d)1ln(ddxxx07.xxde02=218.微分方程1)0(,yyy的特解为xey9.微分方程03yy的通解为xcey310.微分方程xyxyysin4)(7)4(3的阶数为4阶.二、单项选择题(每小题2分,共24分)2.设函数xxysin2,则该函数是(A).A.奇函数B.偶函数C.非奇非偶函数D.既奇又偶函数3.函数222)(xxxxf的图形是关于(D)对称.A.xyB.x轴C.y轴D.坐标原点4.下列函数中为奇函数是(C).A.xxsinB.xlnC.)1ln(2xxD.2xx5.函数)5ln(41xxy的定义域为(D).A.5xB.4xC.5x且0xD.5x且4x6.函数)1ln(1)(xxf的定义域是(D).A.),1(B.),1()1,0(C.),2()2,0(D.),2()2,1(7.设1)1(2xxf,则)(xf(C)A.)1(xxB.2xC.)2(xxD.)1)(2(xx8.下列各函数对中,(D)中的两个函数相等.A.2)()(xxf,xxg)(B.2)(xxf,xxg)(C.2ln)(xxf,xxgln2)(D.3ln)(xxf,xxgln3)(9.当0x时,下列变量中为无穷小量的是(C)A.x1B.xxsinC.)1ln(xD.2xx10.当k(B)时,函数0,0,1)(2xkxxxf,在0x处连续.A.0B.1C.2D.1211.当k(D)时,函数0,0,2)(xkxexfx在0x处连续.A.0B.1C.2D.312.函数233)(2xxxxf的间断点是(A)A.2,1xxB.3xC.3,2,1xxxD.无间断点1.函数2)1(xy在区间)2,2(是(D)A.单调增加B.单调减少C.先增后减D.先减后增2.满足方程0)(xf的点一定是函数)(xfy的(C).A.极值点B.最值点C.驻点D.间断点3.若xxfxcose)(,则)0(f=(C).A.2B.1C.-1D.-24.设yxlg2,则dy(B).A.12dxxB.1dxxln10C.ln10xxdD.1dxx5.设)(xfy是可微函数,则)2(cosdxf(D).A.xxfd)2(cos2B.xxxfd22sin)2(cosC.xxxfd2sin)2(cos2D.xxxfd22sin)2(cos6.曲线1e2xy在2x处切线的斜率是(C).A.4eB.2eC.42eD.27.若xxxfcos)(,则)(xf(C).A.xxxsincosB.xxxsincosC.xxxcossin2D.xxxcossin28.若3sin)(axxf,其中a是常数,则)(xf(C).A.23cosaxB.ax6sinC.xsinD.xcos9.下列结论中(B)不正确.A.)(xf在0xx处连续,则一定在0x处可微.B.)(xf在0xx处不连续,则一定在0x处不可导.C.可导函数的极值点一定发生在其驻点上.D.若)(xf在[a,b]内恒有0)(xf,则在[a,b]内函数是单调下降的.10.若函数f(x)在点x0处可导,则(B)是错误的.A.函数f(x)在点x0处有定义B.Axfxx)(lim0,但)(0xfAC.函数f(x)在点x0处连续D.函数f(x)在点x0处可微11.下列函数在指定区间(,)上单调增加的是(B).A.sinxB.exC.x2D.3-x12.下列结论正确的有(A).A.x0是f(x)的极值点,且f(x0)存在,则必有f(x0)=0B.x0是f(x)的极值点,则x0必是f(x)的驻点C.若f(x0)=0,则x0必是f(x)的极值点D.使)(xf不存在的点x0,一定是f(x)的极值点1.下列等式成立的是(A).A.)(d)(ddxfxxfxB.)(d)(xfxxfC.)(d)(dxfxxfD.)()(dxfxf2.若cxxxfx22ed)(,则)(xf(A).A.)1(e22xxxB.xx22e2C.xx2e2D.xx2e3.若)0()(xxxxf,则xxfd)((A).A.cxxB.cxx2C.cxx23223D.cxx23232214.以下计算正确的是(A)A.3ln3dd3xxxB.)1(d1d22xxxC.xxxddD.)1d(dlnxxx5.xxfxd)((A)A.cxfxfx)()(B.cxfx)(C.cxfx)(212D.cxfx)()1(6.xaxdd2=(C).A.xa2B.xaaxdln22C.xaxd2D.cxaxd27.如果等式Cxxfxx11ede)(,则)(xf(B)A.x1B.21xC.x1D.21x1.在切线斜率为2x的积分曲线族中,通过点(1,4)的曲线为(A).A.y=x2+3B.y=x2+4C.22xyD.12xy2.若10d)2(xkx=2,则k=(A).A.1B.-1C.0D.213.下列定积分中积分值为0的是(A).A.xxxd2ee11B.xxxd2ee11C.xxxd)cos(3D.xxxd)sin(24.设)(xf是连续的奇函数,则定积分aaxxf-d)((D)A.0-d)(2axxfB.0-d)(axxfC.axxf0d)(D.05.xxdsin22-(D).A.0B.C.2D.26.下列无穷积分收敛的是(B).A.0dexxB.0dexxC.1d1xxD.1d1xx7.下列无穷积分收敛的是(B).A.0dinxxsB.02dexxC.1d1xxD.1d1xx8.下列微分方程中,(D)是线性微分方程.A.yyyxln2B.xxyyye2C.yyxyeD.xyyxyxlnesin9.微分方程0y的通解为(C).3A.CxyB.CxyC.CyD.0y10.下列微分方程中为可分离变量方程的是(B)A.yxxydd;B.yxyxydd;C.xxyxysindd;D.)(ddxyxxy三、解答题(每小题7分,共56分)⒈计算极限423lim222xxxx.解:423lim222xxxx4121lim)2)(2()2)(1(lim22xxxxxxxx2.计算极限165lim221xxxx解:165lim221xxxx2716lim)1)(1()6)(1(lim11xxxxxxxx3.329lim223xxxx解:329lim223xxxx234613lim)3)(1()3)(3(lim33xxxxxxxx4.计算极限4586lim224xxxxx解:4586lim224xxxxx3212lim)4)(1()4)(2(lim44xxxxxxxx5.计算极限6586lim222xxxxx.解:6586lim222xxxxx234lim)3)(2()4)(2(lim22xxxxxxxx6.计算极限xxx11lim0.解:xxx11lim0)11(lim)11()11)(11(lim00xxxxxxxxx21111lim0xx7.计算极限xxx4sin11lim0解:xxx4sin11lim0)11(4sin)11)(11(lim0xxxxx81)11(44sin1lim41)11(4sinlim00xxxxxxxx8.计算极限244sinlim0xxx.解:244sinlim0xxx)24)(24()24(4sinlim0xxxxx16)24(44[lim4)24(4sinlim00xxxsimxxxxx⒈设xxy12e,求y.解:xxxxexexexxey1121212)1(2xex1)12(2.设xxy3cos4sin,求y.解:xxxysincos34cos423.设xyx1e1,求y.解:211121xexyx4.设xxxycosln,求y.解:xxxxxytan23cossin235.设)(xyy是由方程422xyyx确定的隐函数,求yd.解:两边微分:0)(22xdyydxydyxdxxdxydxxdyydy22dxxyxydy226.设)(xyy是由方程1222xyyx确定的隐函数,求yd.解:两边对1222xyyx求导,得:0)(222yxyyyx0yxyyyx,)()(yxyyx,1ydxdxydy7.设)(xyy是由方程4ee2
本文标题:微积分初步形成性考核册答案__
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