讨论[tex=0.571x1.0]CQkpoDeAAI+5FKIfe1wVCA==[/tex]k为何值时，积分[tex=8.143x2.714]e9oQ943V2m5fRKvsnmySKCIPw+Ys6itFOoHwokETrYEs+5bcgDVsq72HXUUtkSF+[/tex]收敛？又为何值时发散？

2022-06-19

讨论[tex=0.571x1.0]CQkpoDeAAI+5FKIfe1wVCA==[/tex]k为何值时，积分[tex=8.143x2.714]e9oQ943V2m5fRKvsnmySKCIPw+Ys6itFOoHwokETrYEs+5bcgDVsq72HXUUtkSF+[/tex]收敛？又为何值时发散？

答案：

答 (1)[tex=1.714x1.0]ZObQbEKQrWhJLtgCtDP7uA==[/tex]时,[tex=9.429x2.714]qN8fOJEmxCPwE8y3sw7Scya48cWw1LJS7Iv2dHXXzbKbD3SA+7UDaPreZBMlUfZ2xxQ3VykIOtuUe6EOEi7C+g==[/tex](2)[tex=2.286x1.214]7pAyafSF/tzirY6P4jmK6Q==[/tex]时 ,[tex=18.071x2.643]pUhP6h2mvwiudF14WfkE+uZhYL4JxLfEVL2hYQN4pulwSRzBQ+l68KovqudAjwSM986BdyCjbS6u5E02q79NbSI77El1qt1bE8ZsixoThwiUYPf+Ctju2AdZah8OVbqsSSQwQjGXpk3+yzwN7MNJ/bWlu/Hundsqj7olhmsVpXr5l3tOVLUYceI4RBCIWILU[/tex][tex=16.786x2.786]CaKi5fyjBbNR+9rVcBDlQX5Lnl2GCcgZgUpydbmbQcoADwljjZnPFY8WQe6+fRxinNbzDPcg6mh5YlXGrpgAD4GDNCYWHcMBkETk1JSSMQjue/4m1kkVr6vwZ4d4nOAK[/tex][tex=16.929x2.643]9YLmYQeSC94Nmio0PLMew+5KvCbnwHFe80SjluKD0qtBBEb3nKAa9Z6ypE/dah9wyy9kFiMaupdqkM2IoNVm+glT5JXVwzHNss8gpW19LTUHaWOJ9whbW+QiJgH4oWRagHMyGnrsaWv8plnaF1ZhwLFzto7OSBuKvD745qt19KM=[/tex][tex=23.214x2.786]9YLmYQeSC94Nmio0PLMew7Kcq8h98szlvsRpvb/akPfO3lRVSUCWC1mNIQboRVvzyPVJv186GKtYgtIv7ux1Yw0kOcbpjy1IF9kzbF2TA3Wh36YBZGI6ZjAE48T6uRsJXyiMCWm1YzjYVe8BXrrawwKY0xsGniFqFoK8uPCQl3SYjxM7hKzu7Vw7fD5bdHJjKcMpyMBGAAHak6L6S5MZ+g==[/tex][tex=22.857x2.714]9YLmYQeSC94Nmio0PLMew/v2vp/Z/cIVeRcFUOlQJ5thrmcaq6Tsq1vabqAKw2zG3vkCl5Mb1EED7+WhuVuOJYUwmPY+mXpyPmAjziDJt56pqjOgMyRkDhqJ8kk7CyMycxp2HO7UqduJVpuC+JiesZvjck45TCbMOioz1oB2wjAreNGdQ9ChCIDapLIYYDyymDDKRCd0MgyXhF1cp69cPg==[/tex]于是[tex=18.786x2.643]vFe0TosRGcZL63h4U4acxoUs0s/sOC+FFZF/wgi37wF7+saUB2lAUmYlwDSefnge160eIQ8fE6TWRvoJ63uFDCYfpwiBmL/I5NnjiH/UQweDffgOPjNP7uRDW1VRYkTSlvPDUFW4FNDVxf7uQNPS1g==[/tex][tex=26.357x6.071]ifE9NWj3X6IpRVSt3T5ITpw9pfVSEgatlhcSUHvo2oHWdybYOxKdf2YK0oyycwmnr/MdAY9/LeBAp4k/ejAHu4JGOV7ssdYWiT5WwpQtieV06vjROcMRS1x4ybknFR006ZNEu126tFWdzQW4kktsxhb8FH9vXdoUhIuLLP+G/0nOVIOE6cNxIqH3HhKbkv50ms8LNXA/3rniVgO7JKptL+icwS0RwMfvQRUySA1OmGwLLo3jt+afsfrdjqdKxFScp+7M2YkeQAseNCM8udbvufScdtExr77Aq+CHBcU4nn149HhnxY46A2q4zPt71kL66bjtdbov8OZ6HTXhjzazf6X3NlTgNKci7TIzD973FkwNqfWysyHAZPruslYN20IcHWeunQFphLYFufjY/D4YgdvgZqiqbfGGu3d4wCoa5MY=[/tex]①[tex=29.071x2.786]WEf2nUT4x29AbUUUDPGufNjqic4iKmR0EE8lHYsY02OZZXEiwAWJEkH+OiIL+xNudG1CIAZld0/EgmKhp7zY+/SUFKHqyQ0oVkDtMbz9g1bu967Qt/+EuzPAjZXVuD4sGDOTPT0RP+NW/80pfRI6Qceyqa8wGwVeJr61UOe5lZ1ynTLpqO26EZql87YkKWKoyZeLJyWEdKam5rfuQFpNYGO8D42nxNS4A6S9IPp4xpjVC7TaBBV9DLr2Px3w4tA7tBOxUjPSXn43mrL7PJHNug==[/tex]不存在,则[tex=8.071x2.714]qN8fOJEmxCPwE8y3sw7Scya48cWw1LJS7Iv2dHXXzbLbkwM7E9A2PYc6igvlAuKstTdjtXtOlFK7dNmcgGTxmg==[/tex]发散②[tex=19.929x2.786]wOhei3OZbfHF8mF3jyiYReC4vJMHqpzUr6RqvQI+yfznIeL05tdj5gGOy5q/oNNFYKYRykLhnSbDIq2FQhNR9N9l1We00PmgevQ9DBunHS+ZdcgyWk3Rdn+kVo7nM3wjClY13WPPAe1ytmuqBrMjCD63n2yY7irAHGqia1P9m7r8tHtZEaEscGq4k2BSVCAj[/tex] 不存在,则 [tex=8.214x2.714]qN8fOJEmxCPwE8y3sw7Scya48cWw1LJS7Iv2dHXXzbKbD3SA+7UDaPreZBMlUfZ2zQitfL8BRzVmG0JshyB5YQ==[/tex] 发散;③[tex=23.786x2.786]0UuX1W9BXDPJRLFwV6lpXY5dAdSD3l6XqT7qlIL3WmDD7xiOOYkvyvVvlyieAM87dPj7rs/lK8bO6GRP9uLI+NoEcI1DjmTAKNhNy2IYkFHyl5v91Ii7N24bNdOGirjTRuW9ItTi1QHAsZEQpfUl2CDp+qYoK/TDRHXlSswAT1AznZRlzzcIaNqCeE7hGL8LeIglOgzTNN+lY4+4kv/9qQ==[/tex]则 [tex=12.357x2.714]qN8fOJEmxCPwE8y3sw7Scya48cWw1LJS7Iv2dHXXzbKbD3SA+7UDaPreZBMlUfZ20S8J+2+ClNua9mBIL3YmICf8/CLF1O0QtqRpYOdxD9nJGn4Xurz+wzffBzqM7GN8[/tex]综上(1)[tex=1.714x1.0]ZObQbEKQrWhJLtgCtDP7uA==[/tex]时,[tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex]为任何值积分[tex=8.214x2.714]qN8fOJEmxCPwE8y3sw7Scya48cWw1LJS7Iv2dHXXzbKbD3SA+7UDaPreZBMlUfZ2zQitfL8BRzVmG0JshyB5YQ==[/tex]均收剑(2)[tex=2.286x1.214]7pAyafSF/tzirY6P4jmK6Q==[/tex]时,[tex=2.357x1.143]P0E3IICALVQSPT9L9G2/TA==[/tex]时积分[tex=8.214x2.714]qN8fOJEmxCPwE8y3sw7Scya48cWw1LJS7Iv2dHXXzbKbD3SA+7UDaPreZBMlUfZ2zQitfL8BRzVmG0JshyB5YQ==[/tex]发散;[tex=2.357x1.071]5rNktakNN+GFOjHmGR8RDw==[/tex]时积分 [tex=8.071x2.714]qN8fOJEmxCPwE8y3sw7Scya48cWw1LJS7Iv2dHXXzbLbkwM7E9A2PYc6igvlAuKstTdjtXtOlFK7dNmcgGTxmg==[/tex]收敛.

举一反三

内容

0
当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时，反常积分[tex=6.071x2.429]QDF3on418hztfquUcJypQYwtonQ+mFtQedEGxyAzTPBBJauFsgD+wTUcaYY8YVBM7TsP3lo1GIiuciBXniPdXw==[/tex]收敛？当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时，这反常积分发散？又当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时，这反常积分取得最小值？
1
当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时，广义积分[tex=6.071x2.429]p0+OH7YNKfNLWlS8e6PskjUtyopvOuo/tvBuTNUeY6PJxrsQc3E/JydvDYEgBDy6YEPU2lfw+ksgLS+lm6P50A==[/tex]收敛？当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时，这广义积分发散？又当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时，这广义积分取得最小值？
2
设[tex=23.714x1.357]F78LnNyDYWMwT45phVGkpXmRoKKv1KoK50IIgDInIw5ZFwNSPxgwxej8EZVtYrX5WipJn/IaQh5LMQ4ZkGjoaGA2Un69/jXsXpYJS+JmebD0VXEseX1NdUn5KEUi/GVX[/tex]，试问：（1）a为何值时，[tex=2.429x1.0]xJr2ny42kcAcTeyzkoXuGtgplTUAoUg88inuy+tLeOI=[/tex]线性相关、线性无关？（2）a为何值时，[tex=3.929x1.0]F4n/gPBEEptsP2lf6G/nrvezdRLHToZYZQgLk0DjpQw=[/tex]线性无关？（3）a为何值时，[tex=5.357x1.0]F4n/gPBEEptsP2lf6G/nrpQfb389DliGni4+CvHKoG3s09dl3aIW9JhqBDlIziVL[/tex]线性无关？
3
k为何值时，[tex=7.429x3.929]Uyz5s0rmQIddjb5Jc2T/YTpBoRm8xUYtAqE7zEpoOJP4k8mKUrvyGR6A3h+spGzME/PwE6KN5aUCGnwQdSxmqQ2JENY9S5kMbpxvHY+IbymO+vH8+4xrdLN0OAHqpAuh[/tex].
4
k为何值时，[tex=7.429x3.929]Uyz5s0rmQIddjb5Jc2T/YTpBoRm8xUYtAqE7zEpoOJP4k8mKUrvyGR6A3h+spGzME/PwE6KN5aUCGnwQdSxmqQ2JENY9S5kMbpxvHY+IbymO+vH8+4xrdLN0OAHqpAuh[/tex].