1 . 已知函数
且
.
(1)当
时,讨论函数
的奇偶性;
(2)从①②两组条件中选取一组作为已知条件,证明:
为增函数.
①
;
②
.
注:如果选择两组条件分别解答 ,按第一个解答计分 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2cbb8ec1c9ffc575c51f8de7842446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ac7e26bf11b905a339449befa3a26d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9747ff3a5c251ad95939e2eedbd7b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)从①②两组条件中选取一组作为已知条件,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4591058e231ab65c4ca7aa6775b4e22.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e33cca43018f4a1d93f752c3c034069.png)
注:
您最近一年使用:0次
2 . 已知函数
.
(1)用定义法证明:函数
在区间
上单调递增;
(2)判断函数
在
上的零点个数(不需要证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f477b7be0db85fa9396cc10aa39ef28a.png)
(1)用定义法证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
您最近一年使用:0次
3 . 在四棱锥
中,底面
为矩形,
,平面
平面
,点
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/6b886c6d-76ef-4db3-a3d2-958428ee7838.png?resizew=151)
(1)证明:
;
(2)若
,四棱锥
的体积为
,求直线
与平面
所成角的余弦值.
![](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/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/6b886c6d-76ef-4db3-a3d2-958428ee7838.png?resizew=151)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b503c5da1208576c9fabd3685153c9d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee76246dee4f1670e4f21e5eb393b52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519bd215d019509fa2d88e57f145a896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
9-10高二下·河南·期中
名校
4 . 已知数列
满足
.
(1)写出
,并推测
的表达式;
(2)用数学归纳法证明所得的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf732764ecee2b555071ed13cafae93.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)用数学归纳法证明所得的结论.
您最近一年使用:0次
2022-04-23更新
|
458次组卷
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14卷引用:2012-2013学年湖北仙桃毛嘴高中高二上学业水平监测理数学试卷
(已下线)2012-2013学年湖北仙桃毛嘴高中高二上学业水平监测理数学试卷(已下线)2011-2012学年湖北省仙桃市高二下学期期中考试理科数学试卷(已下线)2010年河南省实验中学高二下学期期中考试数学(理)(已下线)2011-2012学年广东省惠阳一中实验学校高二下学期3月月考理科数学(已下线)2011-2012学年浙江省嵊泗中学高二第一次月考数学试卷(7-8班)(已下线)2011-2012学年江苏南通第三中学高二下学期期中考试理科数学试卷(已下线)2012-2013学年福建省泉州一中高二下学期期中考试理科数学试卷(已下线)同步君人教A版选修2-2第二章2.3数学归纳法山东省菏泽市2016-2017学年高二下学期期中考试数学(理)试题高中数学人教版 选修2-2(理科) 第二章推理与证明 2.3数学归纳法辽宁省营口市开发区第一高级中学2017-2018学年高二下学期第二次月考数学(理)试题天津市红桥区2016-2017学年高二下学期期中理科数学试题山西省晋城市泽州县晋城一中教育集团南岭爱物学校2022-2023学年高二上学期第五次调研考试数学试题1.4 数学归纳法(同步练习基础版)
名校
解题方法
5 . 如图,在棱长为2的正方体
中,
为棱
的中点.求证:
![](https://img.xkw.com/dksih/QBM/2021/7/4/2757244182528000/2762803823493120/STEM/544fd13e-dd9e-4737-9988-093f9b47fa33.png?resizew=220)
(1)
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/2021/7/4/2757244182528000/2762803823493120/STEM/544fd13e-dd9e-4737-9988-093f9b47fa33.png?resizew=220)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7542b49ab149f2be8ba6b48392bef1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ffc3552dd835a9ee6022bb11397a1bd.png)
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2021-07-12更新
|
1004次组卷
|
2卷引用:2021年湖北省普通高中学业水平合格性考试数学试题
解题方法
6 . 已知函数
,
为自然对数的底数.
(1)判断
在定义域上的单调性,并证明你的结论;
(2)是否存在
,使
为奇函数?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e78e6aafaaa6d123f86cc81d79e5830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d218992d1942266d7208e476d0c4100.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在三棱锥
中,
平面
,
,
,
分别为
,
的中点.求证
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/4f49693e-bf73-4e62-be0c-6d19e8a48c29.png?resizew=160)
(1)
平面
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/4f49693e-bf73-4e62-be0c-6d19e8a48c29.png?resizew=160)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
您最近一年使用:0次
2020-12-02更新
|
591次组卷
|
3卷引用:2020年湖北省普通高中学业水平合格性考试数学试题
11-12高二下·湖北省直辖县级单位·期中
名校
8 . 如图,在长方体
中,
,
,点
在棱
上移动.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/5/374890b9-d099-4d80-be75-850c5c3ba8d2.png?resizew=182)
(1)证明:
;
(2)
等于何值时,二面角
的大小为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/5/374890b9-d099-4d80-be75-850c5c3ba8d2.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa81c1f81266b4ef3d471bc6bfc38d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35988677892d6ffdf4773f7a861f26a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
您最近一年使用:0次
2016-12-03更新
|
640次组卷
|
7卷引用:2012-2013学年湖北仙桃毛嘴高中高二上学业水平监测理数学试卷
(已下线)2012-2013学年湖北仙桃毛嘴高中高二上学业水平监测理数学试卷(已下线)2011-2012学年湖北省仙桃市高二下学期期中考试理科数学试卷2015届上海市崇明县高三第二次高考模拟考试理科数学试卷(已下线)1.6.1 垂直关系的判定(课时作业)-2018版步步高学案导学与随堂笔记数学(北师大版必修2)四川省阆中中学2019-2020学年高二4月月考数学(理)试题湖南师大附中2020-2021学年高二上学期10月月考(第二次大练习)数学试题广东省揭阳市揭东区2023-2024学年高二上学期期中数字试题