若函数[tex=3.714x1.357]bgW0mXaRlSN8TPLXtqD9/w==[/tex]对任意的实数[tex=0.429x0.929]r8lLiDb0KHTzu/2y/Au89w==[/tex]满足关系式[tex=10.357x1.5]hjHmTMfusPJvi9xryx+Od1hjrwf6wuCVDDJWJ1v0+jFYMiwD/xsyZ5VbAgNUIvGD[/tex]则称[tex=3.714x1.357]RZiGVmriW8hV4LTYDLQPEQ==[/tex]为[tex=0.571x1.0]CQkpoDeAAI+5FKIfe1wVCA==[/tex]次齐次函数,设[tex=3.714x1.357]RZiGVmriW8hV4LTYDLQPEQ==[/tex]可微,试证[tex=3.714x1.357]RZiGVmriW8hV4LTYDLQPEQ==[/tex]是[tex=0.571x1.0]CQkpoDeAAI+5FKIfe1wVCA==[/tex]次齐次函数的必要条件是[tex=13.786x2.643]g5gxAglkHDvTL9gINvGhk1Bqk3mQZR7GhuWEFPJMDecoTlYC7Q3R5Cu7wJobKl0C6sVCbk/EUOYwA9vSFg9q18ybL1dh/EQr7pyBk4C+5FiDTlEvrZIqUirulUJK4J1tIpiWzULYgnjJBkEw1yh+HA==[/tex] 对任意的 [tex=2.929x1.357]8sXOVKPrSl7odQ08YRvxPw==[/tex] 成立, 反之如何?

2022-05-27

若函数[tex=3.714x1.357]bgW0mXaRlSN8TPLXtqD9/w==[/tex]对任意的实数[tex=0.429x0.929]r8lLiDb0KHTzu/2y/Au89w==[/tex]满足关系式[tex=10.357x1.5]hjHmTMfusPJvi9xryx+Od1hjrwf6wuCVDDJWJ1v0+jFYMiwD/xsyZ5VbAgNUIvGD[/tex]则称[tex=3.714x1.357]RZiGVmriW8hV4LTYDLQPEQ==[/tex]为[tex=0.571x1.0]CQkpoDeAAI+5FKIfe1wVCA==[/tex]次齐次函数,设[tex=3.714x1.357]RZiGVmriW8hV4LTYDLQPEQ==[/tex]可微,试证[tex=3.714x1.357]RZiGVmriW8hV4LTYDLQPEQ==[/tex]是[tex=0.571x1.0]CQkpoDeAAI+5FKIfe1wVCA==[/tex]次齐次函数的必要条件是[tex=13.786x2.643]g5gxAglkHDvTL9gINvGhk1Bqk3mQZR7GhuWEFPJMDecoTlYC7Q3R5Cu7wJobKl0C6sVCbk/EUOYwA9vSFg9q18ybL1dh/EQr7pyBk4C+5FiDTlEvrZIqUirulUJK4J1tIpiWzULYgnjJBkEw1yh+HA==[/tex] 对任意的 [tex=2.929x1.357]8sXOVKPrSl7odQ08YRvxPw==[/tex] 成立, 反之如何?

答案：

必要性：任意取定[tex=3.929x1.357]EZ1YLh+FMEcQAjNnWDBjTOqVbHZPzjlLAW9+eUrkaAaZTW43KRqwtqFsFTvFDbu/[/tex],考虑函数[tex=15.357x1.5]uer7AppChRaWPjWYoRpmjiKRDTedi9U5YieFWAff/QZogNh5fAYaMrkLVHIvC8Myesp7+pYUC3tUmXz8cRCbLbqf2vELpUzraqRpu+AcGKLBYeYUEOTtQkg79kQ2U0lsE+HmwhznTwfAJOncJmEb6w==[/tex]显然        [tex=11.714x2.429]eSQGtNAShC0fG0saOodoN69GbY2Q2SxRRKz5Id+KT3MwLsnJr4/XSxVpoKrDjMT+3oJ9btXHZ4ywwkFF7xqS4AroAXNQsZa+rEnFVsYTrdFkDcLj3aTSDOStp0TCnPYGbFVAhDntS1Znv76P6Sv/Zw==[/tex]              [tex=17.214x2.643]jlvMYrstu4kC4ItOX2zjXPfITd7KK99r5QSK3l2IKx6b0pJiEbfsY2Nw3Zsxx0sX2m9wcJseyd5gEJBP+DU9vTZ3HvWljurqVfbkz7lSqVTWCx2GtxBXLohhlWojU2cppQUZijduqJOzIVK9AcBASEydrLFVkEAcyaIWTAv/FdfAG9V81dRvkaPvIUoAjM7TF8D0A/e+e7nLeEoceGJHig==[/tex]       取 [tex=1.929x1.214]yQDhkQ1pcApEhxzKfltr0w==[/tex] 得[br][/br]      [tex=23.0x4.357]qeiYnKXLEhyhuGRg8yLtr8ORMlRGy/NaJp0nLCwI53Yra9HjGmfXGPwfIvSmI5V5uWH/vR7ZMkH+Ahn6TuYU/JaYZQj9KmGDLRBG41oFNg8zfIhugXiDerRF7gGbcgL+pcG9OWbdD/lrYmpEU01uyqpKu1vKydKToYDy0U27O2EwdA8iejTvLVoBp/DKS5M9Cwzy79TjbstUa0v5fKqma1kzcTFwiCh0rMfdpcGo/K0nXe4VTm9zIZMYB8rRch+OveXpKR5Dpxup6txQsqlkMQ3z3HFeR41gr6QAxsTQ7+366Bb5CwIOg5quw/86o42jf4uxFSHBbAswyRdkGnMUUDdzOTbnyX3rxaivFCMDj7pzZ01J1WyR1gFPAAihtvxPEgU1a+FQ7zO9paJBeO0m8Q==[/tex]      由 [tex=3.929x1.357]EZ1YLh+FMEcQAjNnWDBjTOqVbHZPzjlLAW9+eUrkaAaZTW43KRqwtqFsFTvFDbu/[/tex]的任意性知       [tex=12.643x2.643]g5gxAglkHDvTL9gINvGhk1Bqk3mQZR7GhuWEFPJMDecoTlYC7Q3R5Cu7wJobKl0C6sVCbk/EUOYwA9vSFg9q18ybL1dh/EQr7pyBk4C+5FiDTlEvrZIqUirulUJK4J1tiORfdK9rI37+dElpYiJpiA==[/tex]       反之并不一定成立.例如 [tex=11.929x2.214]5cZHKKGGwJjkhL5OmNYKkSGuB2Qv6myDne1Ad5iVI162PrmlqFp0N9/q+DU9H7Qv/0EexHLLWeMzRj0oY1bUfg==[/tex] 满足[br][/br]          [tex=13.5x2.643]UaJ0aCuFEnRXJQdXL/tbV04m8x5rhf3yhlKB2ZTUz1OzQvhf5LJXPfOLl+bGArmOJpq0Nd467kWA9A1ro4lwiNJ+sFMCdweV2LEMWglacZtbACg3vn+Y8wfrFPhMzQoq56FcaRWLP5Hf/Q9DT3Q8QLgWSxp/Glhr2lEU5QYfwV0=[/tex]但[tex=3.714x1.357]RZiGVmriW8hV4LTYDLQPEQ==[/tex] 不是 3 次齐次函数, 因为此时[br][/br]                           [tex=10.571x1.5]lEVGd/yI25QCmb/FBOa7ERms3PiyHLpVzgkPpYPVz4ENZMynq5mO0ndirfoQ9js4[/tex].

举一反三

内容

0
set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
1
判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]
2
对 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]的不同值，分别求出循环群[tex=1.143x1.214]StMMJ6qThnpokZJIPGrdFyP3vrLnUdltYxmLxjw8za8=[/tex]的所有生成元和所有子群。(1) 7; (2) 8; (3)10 ;(4) 14 ; (5) 15 (6) 18 。
3
设[tex=5.214x1.214]l2vYijvwphpA0Bdo8olvNhKvOVd4RCELKut0jj6S5qs=[/tex]是连续映射，Y是Hausdorff空间，证明：（1）集合[tex=9.357x1.357]QCqopxinhs+TvVYgLw48vVpO4x/Rie4gzAlmw62rJGM=[/tex]是X的闭子集；（2）如果A是X的稠密子集且[tex=3.714x1.357]fo4X83uQk0aLKgSpBjpSMw8oj58YdJ5bCiu5d4gfWQqZvgjwV7CYEcyqXJHmRmoq[/tex]，则f=g。
4
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']