1 . 设数列
的前
项和为
,若
,
.
(1)证明
为等比数列;
(2)设
,数列
的前
项和为
,求
;
(3)求证:
.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5756b52620214f1ead98030c6a7cb81.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b008e35e4367db818d464d31bd2248c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfc690ace28306596f1fa5c88fa3c3d.png)
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2022-05-17更新
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2卷引用:四川省宜宾市第四中学校2021-2022学年高一下学期期中考试数学试题
名校
2 . 已知函数
为奇函数.
(1)求实数
的值;
(2)判断
在
上的单调性,并用定义证明;
(3)若对于任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc25c261cfb3d8134f1681aedb3a52f.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd67623d65571ec957c41057a3182a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-11-28更新
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5卷引用:四川省宜宾市兴文县第二中学校2023-2024学年高一上学期12月月考数学试题
名校
解题方法
3 . 已知函数
是
上的奇函数,
.
(1)求
的值,并证明
的单调性;
(2)若对任意
且
,不等式
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faab0e945072325e609f617aa6a4fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77dd18df997852fec8d7f70c6da67be.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710c6884f20ec5a0000f04ebe1c432e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-25更新
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248次组卷
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2卷引用:四川省宜宾天立高级中学2023-2024学年高一上学期11月月考数学试卷
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解题方法
4 . 已知函数
是定义域为
上的奇函数,且
.
(1)求b的值,并用定义证明:函数
在
上是增函数;
(2)若实数
满足
,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba41b0595eef5e59cfd8f9cc81dc34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)求b的值,并用定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
(2)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a93955a827b93a0f9adda9d281598d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-09-20更新
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560次组卷
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3卷引用:四川省宜宾市宜宾四中2023-2024学年高一上学期期中数学试题
名校
解题方法
5 . 已知函数
,且满足
.
(1)判断
在
上的单调性,并用定义证明:
(2)设
,若对任意的
,总存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef8ceec2288e3485f893f8eae05fb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7b4663b70702ae74b6b80233c0ee9f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a9e4d1e3248d61979ecbc60ff1ec44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1647deca74be1346f76ac07382917b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0cdf79ec49d52434473ee082eefc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2023-10-31更新
|
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4卷引用:四川省宜宾市叙州区第二中学校2023-2024学年高一上学期期中数学试题
名校
解题方法
6 . 已知
,且
.
(1)证明:
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4d3cd39c23987c9088416ce670a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227d4e6ac62442cfdca656d07ed0b122.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d689b0da0bd4803b3e8a6c69542ae466.png)
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2023-09-28更新
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3卷引用:四川省宜宾市第四中学校2023-2024学年高一上学期10月月考数学试题
解题方法
7 . 已知定义在R上的函数
是奇函数.
(1)判断
的单调性,并用定义证明;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd2347716285d725381ce3925cea6362.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/511f7ebb112f25af6d6e11c1730e683e.png)
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解题方法
8 . 如图,四棱锥P—ABCD中,PA⊥底面ABCD,底面ABCD为菱形,点F为侧棱PC上一点.
(1)若PF=FC,求证:PA∥平面BDF;
(2)若BF⊥PC,求证:平面BDF⊥平面PBC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/cf47b91d-c1f8-4805-aa48-309aa55646c7.png?resizew=159)
(1)若PF=FC,求证:PA∥平面BDF;
(2)若BF⊥PC,求证:平面BDF⊥平面PBC.
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2023-08-02更新
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561次组卷
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5卷引用:四川省宜宾市叙州区第二中学校2022-2023学年高一下学期期末数学试题
四川省宜宾市叙州区第二中学校2022-2023学年高一下学期期末数学试题江苏省南京市六校联合体2021-2022学年高一下学期期末数学试题(已下线)专题强化一 线面、面面的平行和垂直位置关系-《考点·题型·技巧》黑龙江省哈尔滨市宾县第二中学2022-2023学年高一下学期期末数学试题四川省南充市阆中东风中学校2023-2024学年高二上学期第一次段考数学试题
名校
解题方法
9 . 如图,在四边形
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4924cef4ea7427027aa6e1e6901f7df5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/9caa0e56-a9fd-4ac1-a70e-3bb650d6089a.png?resizew=181)
(1)证明
;
(2)设
,求
的最大值,并求
取得最大值时
的值为多少.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4924cef4ea7427027aa6e1e6901f7df5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/9caa0e56-a9fd-4ac1-a70e-3bb650d6089a.png?resizew=181)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40094378a6dbbf2071dabeae711a41a4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d38ab3b6048946e6012099d0f2642d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1884dd7bea1b00c41563bc4abcd9d422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1884dd7bea1b00c41563bc4abcd9d422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2023-05-02更新
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2卷引用:四川省宜宾市叙州区第二中学校2022-2023学年高一下学期期中数学试题
10 . 如图,在几何体
中,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
平面
,四边形
是平行四边形,
,
.
(1)证明:
;
(2)若
,
,
,G为DE上一动点,求直线CG与平面ABF所成角的正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/b7e5a6f6-7ec7-4be4-bc66-ab88f0f0bc6c.png?resizew=225)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f5af7cdf388a47357c119f42140f9e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630d82ae0ed6deb825514e0bc92e74a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6469878a955cc09fac22ba5aea3fb962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58625aa461beef32124a2728a1674c9.png)
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