1 . 如图,在正方体
中,
,
,
分别是棱
,
,
的中点,又
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/19/5885aa87-0d8c-4524-b6f1-11d10e4ae823.png?resizew=221)
(1)求证:平面
平面
;
(2)求直线
与
所成角的余弦值;
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/19/5885aa87-0d8c-4524-b6f1-11d10e4ae823.png?resizew=221)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f79058a6f1268b5b1af757ccecff683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ebf7be76eb49f41bed85431705597b9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cf3a313649d7b92f28dd9fb8c27e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
2022-08-11更新
|
377次组卷
|
2卷引用:重庆市酉阳土家族苗族自治县第三中学校2021-2022学年高一下学期第三次月考数学试题
解题方法
2 . 如图,在三棱锥
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953169238556672/2957121693130752/STEM/42721b43-0eb3-4219-84ea-dd90368e4140.png?resizew=178)
(1)求三棱锥
的体积和表面积
(2)若E、F分别为PA、PB的中点,求证
面EFC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9b8e7befcb7881c294070175b1a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5064f5ce5ac8428e277fd578da84ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d715e6b470395136a6c4215dbe6ff82e.png)
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953169238556672/2957121693130752/STEM/42721b43-0eb3-4219-84ea-dd90368e4140.png?resizew=178)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(2)若E、F分别为PA、PB的中点,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2cfa68b1900da8c1a71dd832872689.png)
您最近一年使用:0次
2022-04-13更新
|
283次组卷
|
2卷引用:重庆市酉阳县第三中学校2021-2022学年高一下学期第二次月考数学试题
解题方法
3 . 如图,在平面四边形APBC中,
,
,
,
.将
沿AB折起得到三棱锥
,使得
.
![](https://img.xkw.com/dksih/QBM/2022/5/13/2978782097760256/2980732350521344/STEM/291c3cd1-a0a1-48bb-8910-9d8fb9decf47.png?resizew=302)
(1)求证:
平面ABC;
(2)若点E在棱
上,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd108abaf2b7fc1d0239b28afcf4ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a606499df4459e5fbd6021c61a805359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec33fd6af9f2d43627d42061e5abbd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad34a693f8fae0c32f2b51d4a61b1de.png)
![](https://img.xkw.com/dksih/QBM/2022/5/13/2978782097760256/2980732350521344/STEM/291c3cd1-a0a1-48bb-8910-9d8fb9decf47.png?resizew=302)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f88842cdaf98f1603aa95f1a6fe1a16.png)
(2)若点E在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca15691dfea154b932004966f2fbca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05faa9dc3d99b201de1af0124e0dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
您最近一年使用:0次
2022-05-16更新
|
556次组卷
|
3卷引用:重庆市酉阳土家族苗族自治县第三中学校2021-2022学年高一下学期第三次月考数学试题
4 . 如图,在三棱锥
中,平面
平面
,且
,
,
,
.点E、F分别为
上的点,满足
,点G为线段
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/c2fbd0d1-3d41-47b2-91be-35c7848f0801.png?resizew=198)
(1)证明:平面
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341e8dae00f6b2abc94199ccfd6cf180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65aff0abef2633a6c96690a43285d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec451c43455189eae382b7709b3ae80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe2686ad073830532a9895dbbbe0aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/c2fbd0d1-3d41-47b2-91be-35c7848f0801.png?resizew=198)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2022-05-16更新
|
603次组卷
|
3卷引用:重庆市酉阳土家族苗族自治县第三中学校2021-2022学年高一下学期第三次月考数学试题
名校
5 . 已知函数
,曲线
在点
处的切线方程为
.
(1)求实数
的值,并证明:对
,
恒成立.
(2)设函数
,试判断函数
在
上零点的个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e643a973cc6912a32b96d1893e54ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96cc2abd23e9e9b92fbf52bc335a5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e601d5f49a28dd69ed4e6fa1bab251.png)
您最近一年使用:0次
2021-05-14更新
|
1209次组卷
|
8卷引用:重庆市酉阳土家族苗族自治县第三中学校2021届高三数学考前猜题卷试题
重庆市酉阳土家族苗族自治县第三中学校2021届高三数学考前猜题卷试题辽宁省朝阳市2021届高三一模数学试题(已下线)专题4.13—导数大题(零点个数问题2)-2022届高三数学一轮复习精讲精练(已下线)预测10 导数的综合应用-【临门一脚】2021年高考数学(理)三轮冲刺过关(已下线)预测10 导数的综合应用-【临门一脚】2021年高考数学(文)三轮冲刺过关甘肃省武威市武威六中2020-2021学年高三第十次诊断考试数学(理)试题陕西省渭南市瑞泉中学2022-2023学年高三上学期第二次教学质量检测理科数学试题福建省连城县第一中学2022-2023学年高二下学期3月月考数学试题
名校
解题方法
6 . 已知函数
,且
.
(1)求
的值,并指出函数
在
上的单调性(只需写出结论即可);
(2)证明:函数
是奇函数;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107cf8d703290d0f4c9149796cba9194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5c80755f525d04bdb2b2b416f21fe9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcf3085400ead842e5813f326834e7c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe02ca9a97e6c7639a05ec62c3004fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
7 . 在三棱柱
中,
底面
,
为正三角形,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/3303edc0-87e8-411c-9280-1fd1d56f92c7.png?resizew=175)
(1)求证:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/3303edc0-87e8-411c-9280-1fd1d56f92c7.png?resizew=175)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3837007567ab66f5cbe93ea39d6b259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453fc545c15300a8b13ee3d59353c682.png)
您最近一年使用:0次
2021-05-14更新
|
671次组卷
|
4卷引用:重庆市酉阳土家族苗族自治县第三中学校2021届高三数学考前猜题卷试题
重庆市酉阳土家族苗族自治县第三中学校2021届高三数学考前猜题卷试题河北省邯郸市2021届高三三模数学试题湖北省2021届高三下学期5月新高考模拟联考数学试题(已下线)考点53 章末检测八-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】
8 . 已知数列
是等比数列,且公比
不等于1,
,数列
满足
.
(1)求证:数列
是等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6407cbb35e575e5b7324e9f3d8f420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbad805fcac1ea944f45d8e4682f8e24.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8dc623a9bac29298adee9a51208790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2021-05-15更新
|
810次组卷
|
3卷引用:重庆市酉阳土家族苗族自治县第三中学校2021届高三数学考前猜题卷试题
11-12高二下·江西抚州·期中
9 . 已知函数
.
(1)当
时,求证:函数
在
上单调递增;
(2)若函数
有三个不同的零点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453a50ad28f1eb3ef4fd2c4260b4d837.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee22eb5a2f387eeb896e10c76bdf54fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2016-12-02更新
|
456次组卷
|
5卷引用:重庆市酉阳第一中学校2023届高三下学期模拟(一)数学试题
重庆市酉阳第一中学校2023届高三下学期模拟(一)数学试题(已下线)2011-2012学年江西省临川十中高二下学期期中考试文科数学试卷(已下线)2013届天津市天津一中高三第四次月考文科数学试卷2017届内蒙古包头市高三下学期第一次模拟考试数学(文)试卷【全国市级联考】广东省深圳市2018届高三高考模拟测试9数学试题