证明定理2.设[tex=0.786x1.0]mfjRqhorWjKnT4vuQia3hQ==[/tex]是一点集，[tex=3.5x1.214]96WndKJeajI5Z4HMn2wdlQ==[/tex]是所有到[tex=0.786x1.0]mfjRqhorWjKnT4vuQia3hQ==[/tex]的距离小于[tex=0.571x1.0]SuCz7Gz6Ns6sQqmz1GoxBw==[/tex]的点[tex=0.643x1.0]tuApZYgUtaac6gdYe6k0Sg==[/tex]作成的点集，即[tex=8.571x1.357]biQgktCt1gWJR30HkZ6lsto2NRCK6pZdBIYxSgOUvhQ=[/tex]，则[tex=0.714x1.0]PNQd3mM4efcuGK7crEaGhQ==[/tex]是开集，且[tex=2.786x1.071]i2ilSWq97XM9RtzNY+NzRASCDI4VZ9bQHu4e8i2nkZ0=[/tex].

2022-06-11

证明定理2.设[tex=0.786x1.0]mfjRqhorWjKnT4vuQia3hQ==[/tex]是一点集，[tex=3.5x1.214]96WndKJeajI5Z4HMn2wdlQ==[/tex]是所有到[tex=0.786x1.0]mfjRqhorWjKnT4vuQia3hQ==[/tex]的距离小于[tex=0.571x1.0]SuCz7Gz6Ns6sQqmz1GoxBw==[/tex]的点[tex=0.643x1.0]tuApZYgUtaac6gdYe6k0Sg==[/tex]作成的点集，即[tex=8.571x1.357]biQgktCt1gWJR30HkZ6lsto2NRCK6pZdBIYxSgOUvhQ=[/tex]，则[tex=0.714x1.0]PNQd3mM4efcuGK7crEaGhQ==[/tex]是开集，且[tex=2.786x1.071]i2ilSWq97XM9RtzNY+NzRASCDI4VZ9bQHu4e8i2nkZ0=[/tex].

答案：

[b]证明.[/b][tex=8.0x1.357]hluM3SjPxgul/Poa9Pxz+eBZ6BGqjMfQ2TRt/AE9/VLY3HZYsQphdHxzsI/Nxry7[/tex].设[tex=6.214x1.357]1Hj53RUaqlvax8milagxBPLRyyuwMLXn6R8YOEe8rXD+uuGSouJix4JLG3q8qwDK[/tex].于是[tex=6.143x1.214]kcZW5SjyVYT9gcUOT1xXBZCtmBq0eCy+p2ZQWIz1Rpmm8WIFUzpSTxS6jXf7lNWg[/tex]，使[tex=8.0x1.357]IR8fe0zHFl8L98H4tOcxzrDKeCb/kpFVc9SfozjSEid1V5B0YGlDvfZm9J8ggOcl[/tex]于是[tex=6.429x2.786]5+Wm020NVrTScDiEiUHqusUuJnwGp42N+Y1qf+AqurSVtTL3GkKKqwP1jIzE7M8iyCqPtMOJdKtyNt97EJ5oBw==[/tex],有[tex=8.0x1.357]ZRttKDGsj9dlHpeN5Jt14WN216Wl/OjcdmYsT7HOcB9L6k+qtBQDb6FO5Pc4miE8[/tex][tex=9.714x4.214]rZM5/OPAdr7aX+kNl9iwpNfDf/USzeKYfsYseSYNqxq+1DJg3RHUAGMfcNeAtOlVVb6Rj0TxkSOo7OUH4n/emUxhSZ5Ki1nXSlVBDaowhIW0oV+aOyxZ4x36YwdVjQtbCnvko5XLAq1l2UEd6u8xiA==[/tex][tex=4.714x2.429]u0XDmOHCAfLAoiH/JH4WhV+3jCDYiVlaUJ7CezYqDzLfJZVJNGI3GdbKWtbSYIv2[/tex]由[tex=0.5x0.786]iDJLmFLxSlW0YkyO/X6Dsqv4QQLWj5etzADb/GvC/y8=[/tex]任意，[tex=12.429x2.429]ZRttKDGsj9dlHpeN5Jt14dJ9ihCDQN/a2X23QFgmjE7kNyNl7eJYM+Bvcoh1WXTgw8K2FPPgxsECn2zM4mc43MCdbOTpWzeOTa3DTdVFhX0=[/tex].于是[tex=7.0x2.786]F/JzbK5ZcybsZ9D3/YyDgdaK4NTIY+H9uoMkIwd9WEPdrlofIjlw9AlYKrJ+fXYbO9ojB+7NgIj+aXak+I1CrQ==[/tex]为开集.[tex=9.357x1.357]hluM3SjPxgul/Poa9Pxz+S5gUxQTEYuTDNisEjhfB2NPzhGjcVmpKQ+i8PC5TnB8[/tex].于是[tex=2.214x1.071]eByD4NG9SLOxBeqq5NOCHp8soF0/DlzyOB5JulO8poI=[/tex].

举一反三

内容

0
已知[tex=5.0x1.286]nNRgYScRPw16N2lBJqtTsA==[/tex]，[tex=5.0x1.286]ZIJz5gTGIgdeWAGMFdoL1A==[/tex]，则[tex=6.214x1.286]wE5wtWoL9HR6uGPZrIzvHA==[/tex]成立的[tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex]值为 A: 1 B: 2 C: 4 D: 6 E: 8
1
证明当[tex=0.786x1.0]mfjRqhorWjKnT4vuQia3hQ==[/tex]是[tex=1.214x1.071]ERAYMLhAZTY9mDX0C5cJmQ==[/tex]中的不可数无穷点集时，[tex=1.071x1.143]g0IbrHa9ffhybTQXy4CAubbbHMTCiuTu1wV7RGCxDd0=[/tex]不可能是有限集.
2
求函数[tex=3.286x1.429]kdT+eIE7CHPynuN6CaN40g==[/tex]（抛物线）隐函数的导数[tex=1.071x1.429]BUw1BPFU3fsJlAl/vt9M9w==[/tex]当x=2与y=4及当x=2与y=0时,[tex=0.786x1.357]Hq6bf3CacUy07X+VImUMaA==[/tex]等于什么?
3
若:(1)函数 f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数;(2)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]有导数;(3)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数及函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数,则函数[tex=5.643x1.357]GmtX7Vop79exGU/rpqXUYw==[/tex]在已知点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]的可微性怎样?
4
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]