解题方法
1 . (1)已知
,求证
;
(2)利用(1)的结论,证明:
(
且
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e793a22eefbb0c5252b15dac42a0769.png)
(2)利用(1)的结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb38b30ef5a3de081c41f92ad2992b7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
您最近一年使用:0次
解题方法
2 . 已知函数
,
.
(1)判断
的奇偶性,并证明;
(2)求证:
在
上是减函数;
(3)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db66d6d64d0b653428886ec34cc9798c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab87accf1942ab80def96d12ef173163.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2a0f02510cbf59115751ba5a6e60d7.png)
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解题方法
3 . (1)
,其中x,y均为正实数,比较a,b的大小;
(2)证明:已知
,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ff50e53d35f0c88f9ba8b5ba681d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec33f3dd246b2deec64c7c40b9b2d663.png)
(2)证明:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ff50e53d35f0c88f9ba8b5ba681d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
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解题方法
4 . 已知
是正实数.
(1)证明:
;
(2)若
,证明:
.
(3)已知
是正数,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98a3635df1a3c8258cd54ed816d9544.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483e8298320b2fe64e3b2dbe845ad115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c533a32a305a8489ded77257f8719c.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e64a8e8e9b6c2f1f4e3fd1829b71eec.png)
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名校
解题方法
5 . 在四面体
中,点H为
的垂心,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/11/6104b9ec-b57c-4e0d-b7b6-aeab1f4512f8.png?resizew=164)
(1)若
,求证:
;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/11/6104b9ec-b57c-4e0d-b7b6-aeab1f4512f8.png?resizew=164)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dee6c1410e79934b560642684807e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2298257c6a39a4ac916cee3858cd10e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2c9c32921b9f678056406dbb27fd9b.png)
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2023-05-20更新
|
506次组卷
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2卷引用:安徽省示范高中培优联盟2022-2023学年高一下学期春季联赛数学试题
名校
解题方法
6 . 已知
均为正实数.
(1)设
,
,求证:
;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333de134fb62d12d1b62f59bab55fbfb.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74110bc818c2f5a53d63451c5251eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436a2732e9c9d5ce401c448cd9de80e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f663a586008ecff29abc4cba5948830.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d957381a6902b4d7192f13043aa6a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660ca2c4e0dc6e567c74066ea95aaeb6.png)
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2022-10-19更新
|
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2卷引用:安徽省马鞍山市当涂第一中学2022-2023学年高一上学期11月第一次月考数学试题
名校
解题方法
7 . 证明下列不等式:
(1)已知
,求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
,求证
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead56bb8f5e7a72e9f8640e795caf68d.png)
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2022-10-08更新
|
244次组卷
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2卷引用:安徽省六安市汇文中学、汇文学校2022-2023学年高一上学期第一次联考数学试题
解题方法
8 . 在四棱锥
中,底面
为平行四边形,
平面
,
,设平面
与平面
的公共直线为l.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/10/0b73214c-947c-4d7d-90a7-598e26d90aef.png?resizew=202)
(1)写出图中与l平行的直线,并证明;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfcf34539673d516eb9b259951a81ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f526e2fe627bb4ddebe708c07d0a22fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59502f452fb6a290484608e65a412df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f526e2fe627bb4ddebe708c07d0a22fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cfd630472bc73bd8c2209376dbe9d1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/10/0b73214c-947c-4d7d-90a7-598e26d90aef.png?resizew=202)
(1)写出图中与l平行的直线,并证明;
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00acc724bbb4569974d4775675a6fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af57d63e83ef0e183add10cd6beec65b.png)
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名校
解题方法
9 . 如图,已知四边形ABCD是平行四边形,点P是平面ABCD外一点,M是PC的中点,在DM上取一点G,过G和AP作平面交平面BDM于GH,H在BD上.
![](https://img.xkw.com/dksih/QBM/2022/4/23/2964390428270592/2965851709530112/STEM/a424408b-2cef-4a24-ba99-dbff1e721d3b.png?resizew=241)
(1)证明:
;
(2)若AB的中点为N,求证:
平面APD.
![](https://img.xkw.com/dksih/QBM/2022/4/23/2964390428270592/2965851709530112/STEM/a424408b-2cef-4a24-ba99-dbff1e721d3b.png?resizew=241)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b364dd4066ce0c2a18c9771e9021769f.png)
(2)若AB的中点为N,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d2bbf2309b4ff8599f57bca4203e90.png)
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2022-04-25更新
|
2255次组卷
|
4卷引用:安徽省阜阳市临泉第一中学(高铁分校)2022-2023学年高一下学期第三次月考数学试卷
名校
解题方法
10 . 已知函数
的定义域是
,对定义域的任意
都有
,且当
时,
,
;
(1)求证:
;
(2)试判断
在
的单调性并用定义证明你的结论;
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938308ceead1a6a87920b457f4646f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309c99d0acad93706ab168d1f9c584bb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c23eb89094be66dc8b8711e5fdb58a4.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0a60c52390a20157e60f33c93f75bc.png)
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2022-04-08更新
|
1896次组卷
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5卷引用:安徽省合肥市第一中学2022-2023学年高一上学期期中教学质量检测数学试题
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