1 . 如图,是一个半圆柱与多面体
构成的几何体,平面
与半圆柱的下底面共面,且
,
为弧
上(不与
重合)的动点.
![](https://img.xkw.com/dksih/QBM/2018/2/11/1879836534120448/1881616677453824/STEM/fd0154f856114808a908a1e26c5f811c.png?resizew=160)
(1)证明:
平面
;
(2)若四边形
为正方形,且
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbafc9deed8366d202f0c6b75f6d97ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a3d5d669ac76a2ffb07da81d949adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://img.xkw.com/dksih/QBM/2018/2/11/1879836534120448/1881616677453824/STEM/fd0154f856114808a908a1e26c5f811c.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbaf84a889666deb1fe3ca86a7a85e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4895f682a46bafd3df522cee827ae2d5.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426744425019d20f317ad4353573a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bdbc5489251b3bd1db479c636cc17ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
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2018-02-13更新
|
525次组卷
|
4卷引用:重庆市外国语学校(四川外国语大学附属外国语学校)2021-2022学年高二上学期9月月考数学试题
2 . 已知数列{
}的首项为1,
为数列{
}的前n项和,
,其中q>0,
.
(Ⅰ)若
成等差数列,求数列{an}的通项公式;
(Ⅱ)设双曲线
的离心率为
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549b17fd03994ba73f3341b7189fc01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168d1aaf6b99875b3c5c84882978e364.png)
(Ⅱ)设双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e692bfc8107c4819e98af3f74c89db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f567549e66b339299dbf8369ab5812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17ceba8160ccefa3c4bccc749491dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7532aa134229978d1e36af60959d237.png)
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2016-12-04更新
|
4196次组卷
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7卷引用:重庆市育才中学2020-2021学年高二上学期10月月考数学试题
重庆市育才中学2020-2021学年高二上学期10月月考数学试题2016年全国普通高等学校招生统一考试理科数学(四川卷精编版)(已下线)专题14 数列综合-五年(2016-2020)高考数学(文)真题分项(已下线)专题19 数列的求和问题-十年(2011-2020)高考真题数学分项(已下线)考点21 数列求和问题-2021年新高考数学一轮复习考点扫描(已下线)2016年全国普通高等学校招生统一考试理科数学(四川卷参考版)专题28数列解答题
名校
解题方法
3 . 已知函数
.
(1)若函数
在定义域内为减函数,求实数a的取值范围;
(2)若函数
有两个极值点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b0269d742c3fc63a13848f54a00530.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e060182e701aeda1409ce218f267cba4.png)
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2023-12-13更新
|
1205次组卷
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4卷引用:重庆市九龙坡区杨家坪中学2024届高三上学期第五次月考数学试题
名校
4 . 已知函数
,
.
(1)求过点
且与曲线
相切的直线方程;
(2)设
,其中
为非零实数,若
有两个极值点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d40624fc4d5a669a76185052ee6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ddac37d332169a34598a63b4634b46.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d836280b3e758c30cbd7e8a5b7fbf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a189cb7a07b2e4634481448b9ad685.png)
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