高数单元测试题

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第二章导数与微分自测题（A）一、选择题1.如果SKIPIF1<0在SKIPIF1〈0处可导,则下列结论中错误的是(）A。SKIPIF1〈0B。SKIPIF1〈0C.SKIPIF1〈0D。SKIPIF1<02。SKIPIF1〈0在点SKIPIF1<0处的导数为（）A.1B。0C。—3。若SKIPIF1<0在SKIPIF1〈0处可导，则a、b分别为A.a=2，b=-1B。a=1，b=2C。a=-2，b=1D。a=2，b=—4。若函数SKIPIF1<0在SKIPIF1〈0处有导数，函数SKIPIF1〈0在SKIPIF1〈0处没有导数,则SKIPIF1<0SKIPIF1<0在SKIPIF1〈0处()A.一定都没有导数B。一定有导数C.恰有一个导数D。至少一个有导数5。SKIPIF1〈0,则SKIPIF1〈0=（）A。SKIPIF1〈0B.SKIPIF1<0C.SKIPIF1〈0D.SKIPIF1〈0二、填空题1。已知SKIPIF1〈0则SKIPIF1〈0____________2。若SKIPIF1<0为可微函数，当SKIPIF1<0是，则在点x处的SKIPIF1〈0是关于SKIPIF1<0的______3.已知SKIPIF1<0且SKIPIF1〈0,则SKIPIF1〈0________4.SKIPIF1<0_________5。函数SKIPIF1〈0在t=2处的切线方程为___________三、综合计算题1。等速旋转的角速度是旋转角与对应时间的比，试给出非等速旋转时角速度的定义。2。设函数SKIPIF1<0试讨论x=0处的可导性。3。设函数SKIPIF1〈0要使SKIPIF1<0在x=1处连续而可导，试讨论a、b应为多少?4.设SKIPIF1<0，求SKIPIF1〈05。求SKIPIF1<06.求SKIPIF1<0，n为常数7。求SKIPIF1〈08。求SKIPIF1<09.求SKIPIF1〈010.求SKIPIF1〈011。求SKIPIF1〈012.求SKIPIF1<0第二章导数与微分自测题（B)一、选择题1。下列哪个选项不是洛尔(Rolle)中值定理成立的条件（)A.SKIPIF1<0在闭区间SKIPIF1〈0上连续；B。SKIPIF1<0在开区间SKIPIF1<0上可导；C。SKIPIF1〈0D.SKIPIF1〈02。如果SKIPIF1<0在SKIPIF1<0处可导，则（）A.SKIPIF1<0B.SKIPIF1〈0C。SKIPIF1<0D.SKIPIF1<03。设SKIPIF1<0,的不可导点为（）A.SKIPIF1<0B.SKIPIF1<0C。SKIPIF1〈0D.SKIPIF1<04。设SKIPIF1<0，则SKIPIF1〈0()A。4B.SKIPIF1<0C.SKIPIF1〈0D。05。函数SKIPIF1<0在点SKIPIF1〈0连续，是SKIPIF1〈0在点SKIPIF1<0可导的（）A.必要不充分条件B。充分不必要条件C.充分必要条件D.既不充分也不必要条件二、填空题1。设SKIPIF1〈0，则SKIPIF1<0=____________2。设函数SKIPIF1<0由函数SKIPIF1〈0所确定，则SKIPIF1〈0=________3。若函数有SKIPIF1〈0，则dy=________4。函数SKIPIF1〈0导数不存在的点为__________5。曲线SKIPIF1〈0在点SKIPIF1<0处的切线方程为____________三、综合计算题1。求SKIPIF1〈02。求SKIPIF1〈03。求SKIPIF1<04。设方程SKIPIF1〈0确定了函数SKIPIF1〈0，求SKIPIF1<05.设方程SKIPIF1<0确定了函数SKIPIF1<0,求SKIPIF1〈06.求曲线SKIPIF1<0在横坐标x=e处对应的切线方程和法线方程7.设抛物线SKIPIF1<0对应于横坐标SKIPIF1<0,SKIPIF1<0两点为SKIPIF1〈0，SKIPIF1<0试求平行于SKIPIF1<0的抛物线的切线方程.8.求SKIPIF1<09.求SKIPIF1〈010。设SKIPIF1<0,试证SKIPIF1〈011.设方程SKIPIF1<0确定了函数SKIPIF1〈0求SKIPIF1〈012。设方程SKIPIF1〈0确定了函数SKIPIF1<0,求SKIPIF1<013。求SKIPIF1〈0

第三章试卷A一、选择题（每题3分共15分）1．下列函数在区间SKIPIF1<0内满足拉格朗日定理条件的是(）（A)y=ln(lnx）（B）y=ln（2SKIPIF1<0x）（C）y=lnx（D)y=SKIPIF1〈04。点(0,1)是SKIPIF1〈0的拐点,则（)（A）SKIPIF1<0（B）SKIPIF1<0为任意值,SKIPIF1<0（C)SKIPIF1<0为任意值（D)SKIPIF1<0为任意值，SKIPIF1<05.极限SKIPIF1<0=（）;（A）1(B)0（C）-1（D）不存在6.函数SKIPIF1〈0（）(A)在SKIPIF1〈0上单调减少(B)在SKIPIF1<0上单调增加（C）在SKIPIF1<0内单调减少(D)在SKIPIF1<0内单调增加10.当SKIPIF1<0>0时，SKIPIF1〈0与1+x的大小关系是(）(A）SKIPIF1<0>1+SKIPIF1〈0(B)SKIPIF1〈0<1+SKIPIF1〈0（C）SKIPIF1<0SKIPIF1<01+SKIPIF1〈0（D)SKIPIF1〈0SKIPIF1<01+SKIPIF1<0二、填空题（每题3分共15分）SKIPIF1<0SKIPIF1<0。2。在SKIPIF1〈0SKIPIF1<03。SKIPIF1<0SKIPIF1<04.SKIPIF1<0.SKIPIF1〈0三、计算题（每题10分共70分）SKIPIF1〈0SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1<016证明方程x5x10只有一个正根17SKIPIF1<0。

第三章试卷B

选择题（每小题3分，共15分)下列函数在SKIPIF1<0上满足罗尔定理条件的是(C）ASKIPIF1<0BSKIPIF1〈0CSKIPIF1〈0DSKIPIF1〈02、曲线SKIPIF1<0的拐点是（B）ASKIPIF1<0BSKIPIF1<0CSKIPIF1<0DSKIPIF1〈03、已知函数SKIPIF1〈0，则SKIPIF1<0有（C）实根A一个B两个C三个D四个4、设函数SKIPIF1<0在SKIPIF1〈0内可导，则在SKIPIF1<0内SKIPIF1〈0是函数SKIPIF1<0在SKIPIF1<0内单调增的（B）A必要非充分条件B充分非必要条件C充要条件D无关条件5、如果SKIPIF1<0，则(B）ASKIPIF1〈0是函数SKIPIF1<0的极大值BSKIPIF1<0是函数SKIPIF1<0的极小值CSKIPIF1<0不是函数SKIPIF1〈0的极值D不能判定SKIPIF1〈0是否为函数SKIPIF1<0的极值

二、填空题（每小题3分，共15分）6、函数SKIPIF1<0在SKIPIF1〈0上满足拉格朗日定理的SKIPIF1<0=7、函数SKIPIF1〈0在闭区间SKIPIF1<0上的最大值点为SKIPIF1<0=8、函数SKIPIF1<0的单调减少区间是9、若函数SKIPIF1〈0在SKIPIF1<0二阶可导，则SKIPIF1<0=10、曲线SKIPIF1<0的铅直渐近线为解答题（每题10分共70分)11、计算SKIPIF1<012、计算SKIPIF1〈013、计算SKIPIF1〈014、计算SKIPIF1<015、设函数SKIPIF1<0在SKIPIF1〈0上连续，在SKIPIF1〈0内可导，且SKIPIF1〈0，证明:存在SKIPIF1〈0，使得SKIPIF1<016、证明：当SKIPIF1〈0时,SKIPIF1〈017、设函数SKIPIF1〈0在SKIPIF1<0的邻域内具有三阶导数，且SKIPIF1<0求SKIPIF1〈0求SKIPIF1<0第四章单元测试题(A）选择题：（每题3分，共15分)（1）如果SKIPIF1<0,则SKIPIF1<0（）A、SKIPIF1〈0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<0（2）下列各式中正确的是()A、SKIPIF1〈0B、SKIPIF1〈0C、SKIPIF1〈0D、SKIPIF1〈0（3）已知SKIPIF1<0，则SKIPIF1〈0（）A、SKIPIF1〈0B、SKIPIF1〈0C、SKIPIF1<0D、不可求（4）在区间SKIPIF1<0内，如果SKIPIF1〈0,则下列各式中一定成立的是（）A、SKIPIF1<0B、SKIPIF1〈0C、SKIPIF1〈0D、SKIPIF1〈0（5)下列表达不正确的是（）A、SKIPIF1〈0；B、SKIPIF1〈0；C、SKIPIF1<0；D、以上各项都不正确.2、填空题：（每题3分,共15分）（1）SKIPIF1<0_____________（2）SKIPIF1<0______________(3）SKIPIF1〈0______________（4）SKIPIF1〈0()SKIPIF1〈0(5)已知SKIPIF1<0，则SKIPIF1〈0______________3、计算下列不定积分：（每题4分，共24分）（1）SKIPIF1〈0（2)SKIPIF1〈0（3）SKIPIF1<0（4)SKIPIF1〈0（5）SKIPIF1〈0（6）SKIPIF1<04、计算下列不定积分：（每题4分，共24分）(1）SKIPIF1<0（2）SKIPIF1〈0(3）SKIPIF1〈0（4）SKIPIF1〈0(5）SKIPIF1〈0(6）SKIPIF1〈05、计算下列不定积分（每题4分，共24分）（1)SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1〈0(4)SKIPIF1〈0（5）SKIPIF1〈0(6)SKIPIF1〈0

第四章单元测试题(B）选择题：（每题3分,共15分）（1）如果SKIPIF1<0,则SKIPIF1〈0(）A、SKIPIF1〈0B、SKIPIF1〈0C、SKIPIF1<0D、SKIPIF1〈0（2)下列各式中正确的是(）A、SKIPIF1<0B、SKIPIF1〈0C、SKIPIF1<0D、SKIPIF1<0（3）已知SKIPIF1〈0,则SKIPIF1〈0（）A、SKIPIF1<0B、SKIPIF1〈0C、SKIPIF1<0D、不可求(4）在区间SKIPIF1〈0内,如果SKIPIF1〈0,则下列各式中一定成立的是（）A、SKIPIF1〈0B、SKIPIF1<0C、SKIPIF1〈0D、SKIPIF1〈0（5）下列表达不正确的是(）A、SKIPIF1<0；B、SKIPIF1〈0；C、SKIPIF1<0;D、以上各项都不正确。2、填空题（每题3分，共15分）(1）SKIPIF1〈0_____________SKIPIF1<0（2）SKIPIF1〈0______________SKIPIF1〈0(3）SKIPIF1〈0______________(4)SKIPIF1<0___________________（5）SKIPIF1<0______________3、计算下列不定积分：(每题4分，共20分）（1）SKIPIF1〈0(2）SKIPIF1〈0(3)SKIPIF1〈0(4)SKIPIF1〈0（5）SKIPIF1<04、计算下列不定积分（每题4分，共24分）（1)SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1〈0（5)SKIPIF1<0（6)SKIPIF1<05、计算下列不定积分(每题4分，共24分）（1)SKIPIF1〈0（2）SKIPIF1〈0（3）SKIPIF1<0（4）SKIPIF1〈0(5）SKIPIF1<0（6）SKIPIF1〈0第五章A卷一、填空题1.SKIPIF1〈0SKIPIF1<02.设SKIPIF1<0SKIPIF1<0则SKIPIF1<0SKIPIF1〈03.已知SKIPIF1<0为偶函数且SKIPIF1〈0,则SKIPIF1<0SKIPIF1〈04。设SKIPIF1〈0则SKIPIF1〈0SKIPIF1<05.反常积分SKIPIF1<0SKIPIF1<0二、选择题1.下列等于1的积分是（）SKIPIF1〈0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1〈0SKIPIF1<02.下列等式正确的是（）SKIPIF1〈0SKIPIF1<0SKIPIF1〈0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1〈03.下列式子正确的是（）SKIPIF1〈0SKIPIF1<0SKIPIF1〈0SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1〈0以上都不对4.下列反常积分中，收敛的是（)SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1〈0SKIPIF1〈0SKIPIF1〈0SKIPIF1<05.曲线SKIPIF1〈0，SKIPIF1<0与坐标周围成的面积是（）SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1〈0SKIPIF1<0SKIPIF1〈0SKIPIF1<0SKIPIF1<0三、计算题1.SKIPIF1<02。SKIPIF1〈03.SKIPIF1〈0，其中SKIPIF1<04.SKIPIF1<05.SKIPIF1〈06。SKIPIF1〈07。已知SKIPIF1<0，求SKIPIF1<08.SKIPIF1<09。SKIPIF1〈0四、应用题求由SKIPIF1<0与直线SKIPIF1<0及SKIPIF1<0所围成平面图形的面积。第五章B卷一、填空题1.若SKIPIF1〈0，则SKIPIF1<0SKIPIF1<02.SKIPIF1<0SKIPIF1<03.SKIPIF1〈0SKIPIF1〈04.设SKIPIF1〈0有连续的导数，SKIPIF1〈0,SKIPIF1<0，则SKIPIF1〈0SKIPIF1〈05。若反常积分SKIPIF1<0,则常数SKIPIF1〈0SKIPIF1〈0二、选择题1.SKIPIF1<0（）SKIPIF1〈0SKIPIF1〈0SKIPIF1〈0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1〈02。设SKIPIF1<0在SKIPIF1〈0上连续，则定积分SKIPIF1〈0（）SKIPIF1〈00SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<03.设SKIPIF1〈0，则SKIPIF1<0（）SKIPIF1<0SKIPIF1〈0SKIPIF1〈0SKIPIF1〈0SKIPIF1<0SKIPIF1〈0SKIPIF1〈0SKIPIF1<04.设函数SKIPIF1〈0，则SKIPIF1<0有（）SKIPIF1〈0极小值SKIPIF1<0SKIPIF1<0极小值SKIPIF1〈0SKIPIF1〈0极大值SKIPIF1<0SKIPIF1〈0极大值SKIPIF1<05.已知SKIPIF1〈0，且SKIPIF1<0，则SKIPIF1<0()SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1〈0SKIPIF1<0SKIPIF1<0SKIPIF1〈0三、计算题1.SKIPIF1〈02。SKIPIF1〈03.SKIPIF1<04.SKIPIF1〈05.SKIPIF1<06.SKIPIF1<07。设SKIPIF1<0，求SKIPIF1<08。SKIPIF1<09。SKIPIF1<0四、应用题平面图形SKIPIF1〈0由抛物线SKIPIF1〈0和SKIPIF1〈0轴围成，试求：（1）SKIPIF1<0的面积(2）SKIPIF1<0绕SKIPIF1<0轴旋转所得旋转体的体积(3)SKIPIF1<0绕SKIPIF1〈0轴旋转所得旋转体的体积

第六章A卷

填空题1。过点(3，-2，2）垂直于平面5x—2y+6z—7=0和3x—y+2z+1=0的平面方程为____。2SKIPIF1〈0SKIPIF1<0_________________.3.过SKIPIF1<0点且平行于向量SKIPIF1<0和SKIPIF1<0的平面方程为__________。4.SKIPIF1<0______________。5。SKIPIF1〈0SKIPIF1〈0________________6.SKIPIF1<0___________________。7.SKIPIF1<0____________。8.SKIPIF1〈0___________.9.设SKIPIF1<0互相垂直，且SKIPIF1<0SKIPIF1<0模等于__________。10．过点（0，2,4)且与平面x+2z=1,y—3z=2都平行的直线是_______________.11。SKIPIF1<0___________________。选择题1．SKIPIF1<0SKIPIF1〈0SKIPIF1<02．SKIPIF1<0SKIPIF1〈0SKIPIF1<03.SKIPIF1〈0SKIPIF1〈04。平面3x—3y—6=0的位置是(A)平行xoy平面(B）平行z轴,但不通过z轴；(C)垂直于z轴;(D）通过z轴.答:（)5．SKIPIF1<0SKIPIF1<0SKIPIF1〈06．SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1〈07。SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1〈0SKIPIF1〈08.SKIPIF1<0SKIPIF1<0SKIPIF1〈09.方程SKIPIF1<0在空间解析几何中表示(A）椭圆柱面，（B）椭圆曲线；（C)两个平行平面,（D)两条平行直线.答：（）10.对于向量SKIPIF1<0，有若SKIPIF1<0,则SKIPIF1<0中至少有一个零向量SKIPIF1〈0SKIPIF1<0SKIPIF1〈011。方程SKIPIF1〈0表示(A)单叶双曲面;(B）双叶双曲面;（C)锥面;（D)旋转抛物面.答:(）12.双曲抛物面(马鞍面)SKIPIF1<0与xoy平面交线是（A)双曲线;(B)抛物线，（C）平行直线；(D）相交于原点两条直线;答()

计算题（本题共6小题,每小题8分，满分48分。）1．SKIPIF1<0SKIPIF1〈02．SKIPIF1〈03。SKIPIF1<0SKIPIF1<04.SKIPIF1<0SKIPIF1<05．SKIPIF1〈0SKIPIF1<06．SKIPIF1〈0SKIPIF1〈0SKIPIF1〈07．SKIPIF1〈0四、证明题：1。SKIPIF1<0SKIPIF1<0SKIPIF1〈0

第六章B卷一、填空题(每小题5分，共25分）1．SKIPIF1<0______________。2．已知向量的始点坐标为，则其终点坐标为_____________，模为_____________．3．过点且垂直于向量的平面方程为_____________．4．在空间解析几何中,方程表示_____________（曲面)．5．设向量的方向角，为锐角，，且，则____________.二、

选择题（每小题5分,共25分）1、直线与平面的关系是（)．A．相交B．重合C．垂直D．平行2、设向量满足，则必有（)（A)(B)(C）（D）。3、点到平面的距离为（）（A)1（B)（C)－1(D)4、点关于平面的对称点是（）（A）（B）（C)(D）5、向量与三坐标轴正向夹角分别为，则的方向余弦中的（）（A）（B）（C）（D）三、计算题（每小题10分,共50分）1、

求过点且垂直于平面和的平面方程．2、一直线在坐标面上，且过原点又垂直于直线，求它的对称式方程3、从点到一个平面引垂线,垂足为点,试求此平面的方程。4、判断直线是否在平面上。5、求直线与平面的交点与夹角。第七章试卷A一、单项选择题(每题3分共15分）1．函数SKIPIF1<0在点SKIPIF1<0处连续是函数在该点可微分的（)（A)充分而不必要条件;（B）必要而不充分条件；（C）必要而且充分条件;(D)既不必要也不充分条件。2．对于二元函数SKIPIF1〈0,下列结论正确的是（).若SKIPIF1<0,则必有SKIPIF1<0且有SKIPIF1〈0;若在SKIPIF1〈0处SKIPIF1〈0和SKIPIF1<0都存在,则在点SKIPIF1<0处SKIPIF1〈0可微；若在SKIPIF1<0处SKIPIF1〈0和SKIPIF1〈0存在且连续，则在点SKIPIF1<0处SKIPIF1<0可微;若SKIPIF1〈0和SKIPIF1<0都存在,则.SKIPIF1<0SKIPIF1<0SKIPIF1〈0.3。设ABCD

4．设SKIPIF1〈0为圆域SKIPIF1<0SKIPIF1〈0，化积分SKIPIF1〈0为二次积分的正确方法是(）。A.SKIPIF1〈0B。SKIPIF1<0C。SKIPIF1〈0D。SKIPIF1〈05．设SKIPIF1〈0,改变积分次序,则SKIPIF1<0（)A。SKIPIF1〈0B.SKIPIF1〈0C。SKIPIF1〈0D.SKIPIF1<0

二、填空题(每题3分共15分)6．设积分区域SKIPIF1〈0,且SKIPIF1<0,则SKIPIF1〈07．设积分区域SKIPIF1〈0为SKIPIF1〈0,SKIPIF1<08．若SKIPIF1<0，则SKIPIF1<09．设SKIPIF1〈0,则SKIPIF1<010.设SKIPIF1〈0为园域SKIPIF1〈0,若SKIPIF1〈0，则SKIPIF1〈0三、计算题(每题10分共70分)11．设SKIPIF1<0,求SKIPIF1〈012．设SKIPIF1〈0，求SKIPIF1<013．设SKIPIF1<014．计算二重积分SKIPIF1<0，其中SKIPIF1〈0是由直线SKIPIF1〈0所围成的闭区域.15．改变二次积分SKIPIF1<0的积分次序。16．计算二重积分SKIPIF1<0其中D：SKIPIF1<0SKIPIF1<017．将周长为SKIPIF1<0的矩形绕它的一边旋转得一圆柱体，问矩形的边长各为多少时，所得圆柱体的体积为最大?

第七章试卷B一、单项选择题（每题3分共15分)1．函数SKIPIF1<0在点SKIPIF1〈0处偏导数存在是函数在该点可微分的(）。（A）充分而不必要条件;(B)必要而不充分条件；(C）必要而且充分条件；（D）既不必要也不充分条件。2.设SKIPIF1<0，其中SKIPIF1<0由圆环SKIPIF1<0所确定的闭区域，则必有（）；A.SKIPIF1<0B。SKIPIF1<0C。SKIPIF1〈0D.SKIPIF1<0，但符号不能确定3。设SKIPIF1<0是由SKIPIF1〈0所围成的闭区域,则SKIPIF1<0（）；A。SKIPIF1〈0B。SKIPIF1<0C.SKIPIF1〈0D。04.设SKIPIF1〈0为连续函数，交换积分SKIPIF1〈0的次序得（).A.SKIPIF1<0B。SKIPIF1<0C。SKIPIF1〈0D.SKIPIF1〈05。二次积分SKIPIF1〈0可以写成_（）A.SKIPIF1〈0B。SKIPIF1<0C。SKIPIF1〈0D.SKIPIF1<0二、填空题(每题3分共15分)6．设SKIPIF1〈0，则SKIPIF1<0______。7．设SKIPIF1<0由曲线SKIPIF1〈0所围成，则SKIPIF1〈08．若SKIPIF1<0，则SKIPIF1<09．设SKIPIF1〈0是由直线SKIPIF1〈0及SKIPIF1〈0所围成的闭区域，则SKIPIF1<0;10。积分SKIPIF1〈0的值等于SKIPIF1〈0三、计算题（每题10分共70分）11、设12、设z=z（x,y）是由方程确定的函数,求13、计算二重积分SKIPIF1〈0，其中SKIPIF1<0是由直线SKIPIF1〈0所围成的闭区域。14、改变二次积分SKIPIF1〈0的积分次序。15、求函数的极值.16、改变二次积分SKIPIF1<0的积分次序。17、从斜边之长为SKIPIF1<0的一切直角三角形中，求有最大周长的直角三角形.

第八章无穷级数单元检测题A卷一、选择题：1．级数SKIPIF1<0收敛的充分条件是（）；A．SKIPIF1<0B．SKIPIF1〈0C．SKIPIF1<0D．SKIPIF1<02．若级数SKIPIF1<0收敛，那么下列级数中发散的是（）；A．SKIPIF1〈0B．SKIPIF1〈0C．SKIPIF1<0D．SKIPIF1<03．SKIPIF1〈0是级数SKIPIF1<0发散的（);A．充分条件B．必要条件C．充分必要条件D．既非充分也非必要条件4．无穷级数SKIPIF1<0收敛的充分条件是（);A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1〈0，且SKIPIF1〈0D．SKIPIF1〈0收敛5．对于级数SKIPIF1〈0,下列结论中正确的是(）；A．SKIPIF1<0时，级数收敛B．SKIPIF1<0时，级数发散C．SKIPIF1〈0时，级数收敛D．SKIPIF1〈0时,级数发散二、填空题:6．调和级数SKIPIF1<0是__________。（填收敛或发散)7．收敛级数SKIPIF1<0的和是_________。8．级数SKIPIF1<0是_________。（填收敛或发散）9．级数SKIPIF1<0是_________.（填收敛或发散)10．幂级数SKIPIF1<0的收敛半径SKIPIF1〈0________。三、计算题:11．判定下列级数的收敛性：（1）．SKIPIF1〈0（2）．SKIPIF1〈0(3）．SKIPIF1<0（4）．SKIPIF1〈012．判定级数SKIPIF1〈0是否收敛，如果收敛，是绝对收敛还是条件收敛？13．求幂级数SKIPIF1<0的收敛域。14．将函数SKIPIF1〈0展开成SKIPIF1<0的幂级数.

第八章无穷级数单元检测题B卷一、选择题：1．级数SKIPIF1<0的部分和数列SKIPIF1<0有界是该级数收敛的（）条件；A．必要不充分B．充分不必要C．充分必要D．既不充分也不必要2．若级数SKIPIF1〈0收敛，则下列结论中，不正确的是（）；A．SKIPIF1<0收敛B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1〈03．设SKIPIF1<0，则下列级数中必定收敛的是（）;A．SKIPIF1〈0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<04．关于级数SKIPIF1<0收敛性的下述结论中，正确的是（)；A．SKIPIF1<0时条件收敛B．SKIPIF1<0时绝对收敛C．SKIPIF1<0时条件收敛D．SKIPIF1〈0时发散5．下列级数中发散的是（）;A．SKIPIF1〈0B．SKIPIF1<0C．SKIPIF1〈0D．SKIPIF1〈0二、填空题：6．对于p级数SKIPIF1<0，当SKIPIF1〈0时是______的,当SKIPIF1〈0时是______的。（填收敛或发散）7．级数SKIPIF1<0是_________。(填收敛或发散）8．级数SKIPIF1<0是_________。（填绝对收敛，条件收敛或发散）9．级数SKIPIF1<0是_________。（填绝对收敛,条件收敛或发散）10．幂级数SKIPIF1<0的收敛半径SKIPIF1〈0________。三、计算题:11．判定下列级数的收敛性:（1)．SKIPIF1〈0（2）．SKIPIF1〈0（3)．SKIPIF1<0（4）．SKIPIF1<012．判定级数SKIPIF1<0是否收敛，如果收敛，是绝对收敛还是条件收敛？13．求幂级数SKIPIF1<0的收敛域。14．将函数SKIPIF1〈0展开成SKIPIF1〈0的幂级数。

第九章自测题A卷选择题：1．方程SKIPIF1<0的通解是（）；SKIPIF1<0.SKIPIF1〈0SKIPIF1<0。SKIPIF1<0SKIPIF1<0。SKIPIF1〈0SKIPIF1〈0。SKIPIF1<02。下列函数中,是微分方程SKIPIF1〈0的解的是（）;SKIPIF1<0。SKIPIF1〈0SKIPIF1〈0。SKIPIF1<0SKIPIF1〈0。SKIPIF1<0SKIPIF1〈0。SKIPIF1〈03．函数SKIPIF1<0是方程（）的解SKIPIF1<0.SKIPIF1<0SKIPIF1〈0。SKIPIF1<0SKIPIF1〈0。SKIPIF1<0SKIPIF1<0。SKIPIF1<04。求微分方程SKIPIF1<0的特解时，