名校
解题方法
1 . 正三棱柱
的底面正三角形的边长为
为
的中点;
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
平面
;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1ebdf74ee45f3736307d4a7e64717f.png)
(3)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1bd8a678857b47bb627e665ce58df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1ebdf74ee45f3736307d4a7e64717f.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
您最近一年使用:0次
解题方法
2 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37602d9cd4957b2b2908c64b466e65a4.png)
,
为棱
的中点,
平面
.
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
(2)求证:平面
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37602d9cd4957b2b2908c64b466e65a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d41056df7af667755afade885de3eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fdb2b9d6a4a54ed1328c5b3adcf7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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名校
3 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b57ed792fb63c756aa4372e501f73cf.png)
(1)证明:
存在唯一的零点
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ce4af9a3c5f7987ddef4988ae0a57.png)
(2)若
的零点记为
,设
,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b57ed792fb63c756aa4372e501f73cf.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ce4af9a3c5f7987ddef4988ae0a57.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e5ad7a134838f6ee246e606a625f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb3c14b2ab08a915682646f3377b7b4.png)
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2023-10-01更新
|
159次组卷
|
3卷引用:福建省漳州实验高级中学2022-2023学年高一创新班上学期期中考试数学试题
福建省漳州实验高级中学2022-2023学年高一创新班上学期期中考试数学试题福建省厦门市厦门二中2023-2024学年高一上学期12月月考数学试题(已下线)专题04 指数函数与对数函数2-2024年高一数学寒假作业单元合订本
名校
解题方法
4 . 问题:已知
均为正实数,且
,求证:
.
证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09f3f04837fc78c3a8cd615d0fa4957.png)
,
当且仅当
时,等号成立.
学习上述解法并解决下列问题:
(1)若实数
满足
,试比较
和
的大小,并说明理由;
(2)利用(1)的结论,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09f3f04837fc78c3a8cd615d0fa4957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ce8e7fbb4c8c728f548bb6c3ae8541.png)
当且仅当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc07ff9c2cb23cfe630c7785ba7ed93b.png)
学习上述解法并解决下列问题:
(1)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2edfccf9159bb4010669e938f788149b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09ffc1644c7029219b88232145abbdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e32a3a39e310fe224a979e0cafce49.png)
(2)利用(1)的结论,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eace9aecb35ea07662a7f4fe7f75a856.png)
您最近一年使用:0次
2023-11-13更新
|
68次组卷
|
2卷引用:福建省厦门大学附属科技中学2023-2024学年高一上学期期中考试数学试题
名校
5 . 已知函数
.
(1)判断函数
的奇偶性,并证明你的结论;
(2)求证:
是R上的增函数;
(3)若
,求m的取值范围.
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c04caf886b24ac9fee263e203e89fc6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872c8367ec27f1fe553d87e5397d236b.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f35c30f027c8d39805c829139fa915d.png)
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2023-01-04更新
|
234次组卷
|
2卷引用:福建省福州市屏东中学2023-2024学年高一上学期10月月考数学试题
名校
解题方法
6 . 如图,四边形
为矩形,且
,
,
平面
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/22/3027928911282176/3030210845450240/STEM/3315c85be91b4a41b26dad8314c5f1de.png?resizew=179)
(1)求证:
;
(2)若点
为
上的中点,证明
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/7/22/3027928911282176/3030210845450240/STEM/3315c85be91b4a41b26dad8314c5f1de.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248ddfad39864ab0e183e01f82859e72.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8badfeb9e7556486e02ab60df4dd32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,四棱锥
中,
,
,E为PB的中点.
平面PAD;
(2)过D点是否存在一个与PA,AB相交,且与平面PBC平行的平面?若存在,指出交点位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4031f4aae0b996ce8fec956fb2879f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f30e54bb771ad15067221459f202f01.png)
(2)过D点是否存在一个与PA,AB相交,且与平面PBC平行的平面?若存在,指出交点位置,并证明你的结论;若不存在,请说明理由.
您最近一年使用:0次
2022-05-04更新
|
984次组卷
|
5卷引用:福建省宁德市同心顺联盟2021-2022学年高一下学期期中联合考试数学试题
名校
解题方法
8 . 选用恰当的证明方法,证明下列不等式.
(1)已知
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbefc06b3b4e54a6a1690e870efc69b.png)
(2)已知a,b,c为正数,且满足
.证明:
;
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a521891098b625f372ff648d110afe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbefc06b3b4e54a6a1690e870efc69b.png)
(2)已知a,b,c为正数,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3681a97ebef383e8968347548102fb49.png)
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2021-11-07更新
|
349次组卷
|
3卷引用:福建省三明市沙县金沙高级中学2022-2023学年高一上学期第一次调研考试数学试题
名校
解题方法
9 . 设
是定义在R上的函数,对任意
,恒有
,当
时,有
.
(1)求证:
,且当
时,
;
(2)证明:
在R上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b8e9b3f07d91da4d256d18df240fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5456d544e2f8d22c08f3ccee002dad4a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c9a7ed0961f8977a21dab37aab396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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21-22高二上·福建厦门·开学考试
名校
解题方法
10 . 如图,已知点P是平行四边形
所在平面外一点,
平面
,M,N分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9da13165-bb73-4ae3-83d7-6e65a4e640be.png?resizew=139)
(1)求证:
平面
.
(2)试在
上确定一点Q,使平面
平面
,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9da13165-bb73-4ae3-83d7-6e65a4e640be.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)试在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d6772f5331cf0cc5302123e4698ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次