解题方法
1 . 如图,正三棱柱
中,
分别是棱
上的点,
.点M为棱
上的动点,满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/0efce3ec-061b-4193-afd2-e9942d9c847a.png?resizew=145)
(1)当
为何值时,直线
平面
,并证明你的结论;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95c0160e73beb94a4a1cbc0168e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e80c9702720a88f4a31c0484c7ff5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172445f5dadf958310b11a6b970bc05b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/0efce3ec-061b-4193-afd2-e9942d9c847a.png?resizew=145)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dbbf1a30ea54a46b903a9645debab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d557872d3299577be8c5872ba1ae5b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8762b26b773a3c41e51d1eb3113169.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)证明
;
(2)关于
的不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e346839e6c4af40f84a2387dafcacd3f.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
(2)关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603feedf045b45e1008cbd9d2b290f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-07-15更新
|
474次组卷
|
3卷引用:江西省南昌市新建区第二中学2024届高三上学期8月份学业水平考核数学试题
名校
3 . 如图,四棱锥
的底面
为平行四边形,
是边长为
的等边三角形,平面
平面
,
,
,点
是线段
上靠近点
的三等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/9bbf75ec-86f5-4976-b078-4d659a9dab48.png?resizew=171)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4edc320c5767838e1761c189b6c48a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9880952857950577055578875ab29141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553d5269397c5cf0909c734464e1b472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dbacc8f5a9d6c606548dc11f19781e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19e44711cb887515d7f75e73845c175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/9bbf75ec-86f5-4976-b078-4d659a9dab48.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c17cbe2d45c8da02c0cb80bf407da9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-10-24更新
|
761次组卷
|
11卷引用:江西省南昌市新建区第二中学2022-2023学年高二上学期10月学业水平考核数学试题
江西省南昌市新建区第二中学2022-2023学年高二上学期10月学业水平考核数学试题江西省南昌市2017届高三第三次模拟考数学(理)试题江西省南昌市2017届高三第三次模拟考理科数学试题【全国百强校】浙江省宁波市镇海中学2019届高三上学期期中考试数学试题浙江省杭州市北斗联盟2019-2020学年高二下学期期中联考数学试题浙江省杭州市富阳区第二中学2020-2021学年高二下学期4月月考数学试题浙江大学附属中学玉泉校区2021-2022学年高二下学期期中数学试题广西壮族自治区南宁高新技术产业开发区桂鼎学校2022-2023学年高二上学期11月期中数学试题山西省阳泉市第一中学校2022-2023学年高三上学期11月期中考试数学试题专题07B立体几何解答题山西省大同市云冈区汇林中学2024届高三上学期期中数学试题
解题方法
4 . 如图,已知多面体
,其中
是边长为4的等边三角形,
平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/5/eaac9db3-afbe-44de-9812-8e1e474bc672.png?resizew=189)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a6b507bfde28bba729352d6fcb925d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b8eec9376f6e6a314da534b095f090.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/5/eaac9db3-afbe-44de-9812-8e1e474bc672.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81fa367ec317fe2a30142e1c30cce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52753d89bf58589e2e83b19bd3d140b8.png)
您最近一年使用:0次
2022-07-29更新
|
1307次组卷
|
4卷引用:江西省南昌市新建区第二中学2022-2023学年高二上学期10月学业水平考核数学试题
名校
解题方法
5 . 如图,在四棱锥
中,底面
为菱形,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2021/1/30/2647227807825920/2652098975727616/STEM/9d1274f7b4894893bd42a2400854de78.png?resizew=237)
(1)求证:
平面
;
(2)若
平面
,
,
,求点B到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2021/1/30/2647227807825920/2652098975727616/STEM/9d1274f7b4894893bd42a2400854de78.png?resizew=237)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5a9a04de2ddcec2b2799ab5476f2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb552b9e21dbaba74d11aa747790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
您最近一年使用:0次
2021-02-06更新
|
977次组卷
|
3卷引用:江西省南丰县第二中学2020-2021学年高一下学期学生学业发展水平测试数学试题
6 . 已知数列
满足:
,
.
(1)证明数列
是等比数列,并求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3998df04d0a8ded946c3f39d545fdc7e.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3c883222af8ff180c92d6261e2a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2021-03-09更新
|
1511次组卷
|
5卷引用:江西省南丰县第二中学2020-2021学年高一下学期学生学业发展水平测试数学试题
江西省南丰县第二中学2020-2021学年高一下学期学生学业发展水平测试数学试题江西省抚州市2020-2021学年高一下学期期末数学试题陕西省安康市石泉中学2020-2021学年高二下学期开学摸底考试文科数学试题陕西省安康市石泉中学2020-2021学年高二下学期开学摸底考试理科数学试题(已下线)突破4.3.1 等比数列课时训练-【新教材优创】突破满分数学之2020-2021学年高二数学课时训练(人教A版2019选择性必修第二册)