解题方法
1 . 已知
的值域为
.
(1)求实数
的值;
(2)判断函数
在
上的单调性,并给出证明;
(3)若
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be8c296dba4a6442f262437f6671c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f3966052d4a779b6247fdf12f97cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb85ae535f90b3c125d86b439ab2562.png)
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解题方法
2 . (1)已知
,求证
;
(2)利用(1)的结论,证明:
(
且
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e793a22eefbb0c5252b15dac42a0769.png)
(2)利用(1)的结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb38b30ef5a3de081c41f92ad2992b7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
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3 . 已知
,
.
(1)求证:
;
(2)证明:若点
在指数函数
的图像上,则对同一个
,点
也在对数函数
的图像上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d4205d528820bc28de45e4378547bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a6e2fbf26c84a3301b5249f70ac8ca.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98f2c47e43878c5ba4feb3b5cc500b9.png)
(2)证明:若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eca933e9678e98c96a35ee03e07d4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d018d0b5d1970404a82d6dc0d5e1771c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
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4 . 已知数列
满足
.
(1)求
的通项公式,并证明:对任意的x>0,有
;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2809a8152b50d110836e9f3672dcb8da.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412344b6c0d2e24e0a3aa490732884ec.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db043bcbb8ca1a51370497ba507f34a0.png)
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名校
5 . 如图,多面体ABCDE中,四边形ABED是直角梯形,∠BAD=90°,DE∥AB,△ACD是的正三角形,CD=AB=
DE=1,BC=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/d89e000f-a5b7-41ba-9631-e0638fd483ee.png?resizew=170)
(1)求证:△CDE是直角三角形
(2) F是CE的中点,证明:BF⊥平面CDE
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/d89e000f-a5b7-41ba-9631-e0638fd483ee.png?resizew=170)
(1)求证:△CDE是直角三角形
(2) F是CE的中点,证明:BF⊥平面CDE
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2019-01-02更新
|
234次组卷
|
2卷引用:【全国百强校】湖南省衡阳市第一中学2018-2019学年高一上学期六科联赛数学试题
6 . 在四面体ABCD中,过棱AB的上一点E作平行于AD,BC的平面分别交四面体的棱BD,DC,CA于点F,G,H
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0eac358e-d7aa-4e75-b4fd-cbe363f87349.png?resizew=152)
(1)求证:截面EFGH为平行四边形
(2)若P、Q在线段BD、AC上,
,且P、F不重合,证明:PQ∥截面EFGH
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0eac358e-d7aa-4e75-b4fd-cbe363f87349.png?resizew=152)
(1)求证:截面EFGH为平行四边形
(2)若P、Q在线段BD、AC上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7071b5ecb076a09f8d128c58f01220ee.png)
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7 . 给定由正整数组成的数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ef842458c67bd274549d90e916e5ac.png)
(1)求证:数列相邻项组成的无穷个整点
均在曲线
上.
(2)若设
,证明:
整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ef842458c67bd274549d90e916e5ac.png)
(1)求证:数列相邻项组成的无穷个整点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4700f448e5e421847effc897502aba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db3ae18875992d69a104310d7b12a6d.png)
(2)若设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbc2f2c80dfac0c350de25cd20e9c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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8 . (1)求证:存在无穷多个正整数
,使得
和
同时是合数;
(2)试判断,是否存在正整数
,使得对于任意正整数
,总有
和
之一为质数?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4477c21464761f33f2868cc1a5ba793d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54ea1748b9fab39aa63880f8144d507.png)
(2)试判断,是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a550c916c64f621010e604a30ef67566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8e87146e09a898de1ba7bf63ab8eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9a5aa985e16243602f536c635cc8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247bbb2271c2b9dd93e9844dd820728b.png)
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9 . 给定双曲线
,过它的一个焦点作直线
,交C于点
分别为C的实轴端点.求证:对于任意满足条件的l,
的交点在一条定直线上,给出该直线方程并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6669e2262175d6d76414c52ae8ade275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59a52c88d08d333fcce816f481011e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbdb45c4a2eda1d98f6bed1e368d015.png)
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