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1、2010年江苏省《高等数学》竞赛试题（本科二级）一填空题（每题4分，共32分）1.2.，3.，4.5.6.圆的面积为7.，可微，，则8.级数的和为.二.（10分）设在上连续，且，求证：存在点，使得.beconsistentwithinthesamedisk.Alternateunifiedcorerequirementsplacedontheterminalstripterminals,onlineidentityandensurethecoppercoreisnotexposed.6.4.6enclosurewithinthe
2、sametothecablecoreprovidesbindingintoacircle,harnesstiespacingisgenerally100mm;branchofficesshallbebindingonbothends,eachcore三．（10分）已知正方体的边长为2，为的中点，为侧面正方形的中点，（1）试求过点的平面与底面所成二面角的值。（2）试求过点的平面截正方体所得到的截面的面积.四（12分）已知是等腰梯形，,求的长，使得梯形绕旋转一周所得旋转体的体积最大。beconsistentwithinthesame
3、disk.Alternateunifiedcorerequirementsplacedontheterminalstripterminals,onlineidentityandensurethecoppercoreisnotexposed.6.4.6enclosurewithinthesametothecablecoreprovidesbindingintoacircle,harnesstiespacingisgenerally100mm;branchofficesshallbebindingonbothends,eachcor
4、e五（12分）求二重积分，其中六、（12分）求，其中为曲线从到.beconsistentwithinthesamedisk.Alternateunifiedcorerequirementsplacedontheterminalstripterminals,onlineidentityandensurethecoppercoreisnotexposed.6.4.6enclosurewithinthesametothecablecoreprovidesbindingintoacircle,harnesstiespacingisgen
5、erally100mm;branchofficesshallbebindingonbothends,eachcore七.（12分）已知数列单调增加，记，判别级数的敛散性.beconsistentwithinthesamedisk.Alternateunifiedcorerequirementsplacedontheterminalstripterminals,onlineidentityandensurethecoppercoreisnotexposed.6.4.6enclosurewithinthesametothecable
6、coreprovidesbindingintoacircle,harnesstiespacingisgenerally100mm;branchofficesshallbebindingonbothends,eachcore2008年江苏省普通高等学校非理科专业一、填空题（每小题5分，共40分）1）时，2）3）设则4）时，在时关于的无穷小的阶数最高5）6）7）设则8）设为所围区域，则二、（8分）设数列为：，求证：数列收敛，并求其极限beconsistentwithinthesamedisk.Alternateunifiedcore
7、requirementsplacedontheterminalstripterminals,onlineidentityandensurethecoppercoreisnotexposed.6.4.6enclosurewithinthesametothecablecoreprovidesbindingintoacircle,harnesstiespacingisgenerally100mm;branchofficesshallbebindingonbothends,eachcore三、（8分）设函数在上连续求证：存在使得四、（8
8、分）将平面上的曲线绕直线旋转一周得到旋转曲面，求此旋转曲面所围立体的体积.beconsistentwithinthesamedisk.Alternateunifiedcorerequirementsplacedontheterminalstripterminal
