1 . 已知有限集
(
).如果A中的元素
(
)满足
,就称A为“复活集”,给出下列结论:
①集合
是“复活集”; ②若
,且
是“复活集”,则
;
③若
,则
不可能是“复活集”;④若
,则“复活集”A有且只有一个,且
.
其中正确的结论是__________ .(填上你认为所有正确的结论序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3f090142bfa3bcb90ecdb3ee904e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deeed8d5eefca600669724369678a27.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc508cedd135c79cd3d0c5232de772cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faaab33de7a473d72438f99e0814711c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ed17b083fe22b6f302ee13b7d181d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd2995bc6100a2ba0ff45d28dea41b9.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b92442e3a390779ed8f0e849e65517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ed17b083fe22b6f302ee13b7d181d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f477bb468a7cd2e854d8f9ad848a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
其中正确的结论是
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名校
解题方法
2 . 数列
满足:对一切
,有
,其中
是与
无关的常数,称数列上有界(有上界),并称
是它的一个上界,对一切
,有
,其中
是与
无关的常数,称数列下有界(有下界),并称
是它的一个下界.一个数列既有上界又有下界,则称为有界数列,常值数列是一个特殊的有界数列.设
,数列
满足
,
,
.
(1)若数列
为常数列,试求实数
、
满足的等式关系,并求出实数
的取值范围;
(2)下面四个选项,对一切实数
,恒正确的是.(写出所有正确选项,不需要证明其正确,但需要简单说明一下为什么不选余下几个)
A. 当
时,
B. 当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83ebf3d559b3ccf4427a9464dc9dbd4.png)
C. 当
时,
D. 当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83ebf3d559b3ccf4427a9464dc9dbd4.png)
(3)若
,
,且数列
是有界数列,求
的值及
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cad0f23354aa754ade482d849557fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73702a22abbf58a70e56a40540de7355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)下面四个选项,对一切实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A. 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bd9f5db8b97abf9bdd15b8efb6c64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83ebf3d559b3ccf4427a9464dc9dbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc64eaf4cd6737b000b28f1fcdd16c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83ebf3d559b3ccf4427a9464dc9dbd4.png)
C. 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f06408895febc126c2ae409e807349c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83ebf3d559b3ccf4427a9464dc9dbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cca0ec4b4343a6ccd13b652aea1d00c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83ebf3d559b3ccf4427a9464dc9dbd4.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb6f7b71775c568314728843894813e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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