经济数学基础形成性考核册
作业(2)
一、填空题
1.若?f?x?dx?2x?2x?c，则f?x?? Qf?x???2x?2x?c??2.??sinx??dx?sinx?c2xln2?2
?F?e?x??c3.若?f?x?dx?F?x??c，则?e?xf?e?x?dx? ?ef?e?x?x?x?x?x?dx???f?e?d?e???F?e??c0
4.设函数Qde2ln1?xdx????1dx?e1ln?1?x2?dx是一个常数0
5.若P?x???Q设11?t211?t2xdt，则P??x???11?x20x的原函数为F?t?,则P?x??F?t?t?x?F?0??F?x?
?P??x??0?F??x??F??t?二、单项选择题
??11?x21.下列函数中，?D?是函数xsinx2的原函数1 A.cosx22B.2cosx2C.?2cosx2 12D.?cosx22.下列等式成立的是?C?1?1? A.sinxdx?d?cosx?B.lnxdx?d??C.2xdx?d?2xln2?x??D.1xdx?dx3.下列不定积分中，常用分部积分法计算的是?C? A.?cos?2x?1?dxB.?x1?xdx2C.?xsin2xdx xD.?dx1?x24.下列定积分计算正确是?D? A.?2xdx=2B.?dx=15C.??1?1116?2??2sinxdx?0D.?sinxdx?0???
5.下列无穷积分中收敛的是?B? A.???11dxxB.???11dxx2C.?edx0??xD.?sinxdx1??
三、解答题
1.计算下列不定积分
?3?x??3x3xe??3??(1)?xdx????dx??c?x?c
3ee?ln3?1??e?lne(2)???x?1?x?2x1?2x?x2xdx41?1?dx????2x?x?dx?2x?xx?x2?c32?x?
?x?2??x?2?x2?41(3)?dx??dx???x?2?dx?x2?2x?c
x?2x?22(4)?1111dx???d?1?2x???ln1?2x?c 1?2x21?2x223112222(5)?x2?xdx??2?xd?2?x?dx??2?x??c
23(6)?sinxxdx?2?sinx2xdx?2?sinxdx??2cosx?c
xxx(7)?xsindx??2xcos?4sin?c222x(?)xsin2
x(?)1↘?2cos2x(?)0↘?4sin2(8)?ln?x?1?dx?xln?x?1???xdln?x?1?xdxx?1
1???xln?x?1????1??dxx?1??1?xln?x?1???1dx??d?x?1?x?1?xln?x?1??x?ln?x?1??c?xln?x?1???2.计算下列定积分
2121??(1)?1?xdx???1?x?dx???x?1?dx??x?x2??1?112??1?1?1???x2?x??2?21?5 2(2)?(3)?21e32e1?x?dx??ed??ex??2?1x?x?1x1121?e?e d?lnx?1??21?lnx?20e311x1?lnx1dx?2?e31121?lnx?2
1?1?(4)?2xcos2xdx??xsin2x?cos2x?04?2?(?)xcos2x1(?)1↘sin2x21(?)0↘?cos2x4(5)?xlnxdx1e???12
1e1??lnxdx2?x2lnx212?e1??4e11?xdlnx??x2lnx2?2?e11?x22e12?e?1??4?(6)??1?xe04?x?dx??404dx??xe?xdx?x0??xe?x?e?x?040?3?3e?4
(?)xe?x(?)1↘?e?x(?)0↘e?x
经济数学基础形成性考核册
作业(3)
一、填空题
?104?5??，则A的元素a?1.设矩阵A??3?23223????216?1??3
2.设A、B均为3阶矩阵，且A?B??3，则?2ABT?2?72
A3.设A、B均为n阶矩阵，则等式?A?B??A2?2AB?B2成立的充分必要条件是AB?BA?也叫A、B可交换?4.设A、B均为n阶矩阵，?I?B?可逆，则矩阵A?BX?X的解X??I?B??1
?100??，则A?1?5.设矩阵A??020????00?3????10??01?2??00??0??0??1???3?
二、单项选择题
1.以下结论或等式正确的是?C?A.若A,B均为零矩阵，则有A?BC.对角阵是对称阵 B.若AB?AC,且A?O,则B?C D.若A?O,B?O,则AB?O 2.设A为3?4矩阵，B为5?2矩阵，且乘积矩阵ACBT有意义，则CT为?B?A.2?4B.4?2C.3?5D.5?3
3.设A、B均为n阶可逆矩阵，则下列等式成立的是?C?A.?A?B??A?1?B?1C.AB?BA 4.下列矩阵可逆的是?A??123??A.?023????003????10?1??11???B.?101?C.?00?????123???11?
D.???22??1B.?A?B??A?1?B?1D.AB?BA ?1
?15.矩阵A???2??1A.0B.1C.2三、解答题 1.计算
?11?0?1??的是?C? ?34??D.3?1????21??01???2?0?1?1?2?1?1?0??1?2? ??????????53??10??5?0?3?15?1?3?0??35?0?1?2?0??00??02??11??0?1?2?0?2????00???0?1???3??00?1???3??0???00? 0?3?????????3??0??????1??3?2?0?5???1??4?2???0? ?3???1254?????1?????2??12.计算???1??1?7 ???7??023???1?122????32????2197??2?6120?????4?7????324??245??610?43?????3?1????3?27??
45??5152??111?10??0????27?????3?2?14???233.设矩阵A???11??0?1?23?1??1??1AB??111?????0?11????0?1??123??112?，求AB1?，B??????1??011??
23??5611??246?,AB?012?????????10?1??11?
电大数学形成性考核作业答案完整版准确版
