解题方法
1 . 已知函数
.
(1)当
时,证明:
;
(2)已知
,
,求证:函数
存在极小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d44d5e638a975bc93491659a141d8c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29cee707aaa2ee5798e38b9624dc396e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80cd7a435009b8713641e5ff655179a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb319ba3ed05f5ad4c9f56b40e43e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)求证:函数
是定义域为
的奇函数;
(2)判断函数
的单调性,并用单调性的定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbd9e52b79fb84c320dc522e13d4f0b.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2024-01-24更新
|
652次组卷
|
4卷引用:江西省上饶市婺源天佑中学2023-2024学年高一上学期1月考试数学试题
名校
解题方法
3 . 已知函数
.
(1)判断
在
上的单调性,并证明;
(2)若
,且
,
,
都为正数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b639ac9599358d08bd6e1c389ceb4.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5087c6cffc4d06a642c80266779bc1ab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583ba1df9316494e286f550b2a35d31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bb9ae14a9495733d41f701b674a7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38308e27660bfabc1ae926615e05451d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff80ea83b3eed82989727032891f16fd.png)
您最近一年使用:0次
2024-01-26更新
|
193次组卷
|
2卷引用:江西省上饶市广丰中学2023-2024学年高一上学期期末数学试题
名校
解题方法
4 . 若函数
在定义域内存在两个不同的数
,
,同时满足
,且
在点
,
处的切线斜率相同,则称
为“切合函数”.
(1)证明:
为“切合函数”;
(2)若
为“切合函数”(其中
为自然对数的底数),并设满足条件的两个数为
,
.
(ⅰ)求证:
;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecaca8409b3f51d22667a14559c58ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe0de54dfc96a2291e8d5e56676eabc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb46178ba0560d96bd3a05891505b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c20b8bd265b07dd90690ad4e349c6dc.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cde09c609543feedc2e0c11992b2bd.png)
您最近一年使用:0次
2024-01-03更新
|
1030次组卷
|
4卷引用:江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)
江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)重庆市南开中学校2024届高三上学期第五次质量检测数学试题重庆市沙坪坝区南开中学校2024届高三上学期第五次质量检测数学试题(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
名校
解题方法
5 . 选用恰当的证明方法;解决下列问题.
(1)
为实数,且
,证明:两个一元二次方程
,
中至少有一个方程有两个不相等的实数根.
(2)已知:
,且
,求证:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1476efe1fd8970d815af8a6e62d454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341f6b48e2c616585ed9bd7dbb9c8728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3ce04492780c4d40fab17aa28d3755.png)
(2)已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c96a416540d6d2c2570c7106f5e0492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03f1c0c0618a585e86afc523bd523e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356bc29ee1bc3f046d9a7b2804c77cf9.png)
您最近一年使用:0次
2023-10-14更新
|
97次组卷
|
2卷引用:江西省上饶市广丰中学2023-2024学年高一上学期10月月考数学试题
名校
解题方法
6 . 已知a、b为正数.
(1)已知
,求证:
;
(2)若
,证明:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8a8d68c4616b1e49c6556509a6cf84.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de6fcb38854c3d2dd97be5793c61952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30455ba662f60fd9bdb3a18bb526febd.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在三棱柱
中,若G,H分别是线段AC,DF的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
;
(2)在线段CD上是否存在一点
,使得平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
平面BCF,若存在,指出
的具体位置并证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0147945bdf3db4bf5e40be746ef2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)在线段CD上是否存在一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2023-04-13更新
|
3138次组卷
|
9卷引用:江西省宜春市第十中学2024届高二上学期开学检测数学试题
江西省宜春市第十中学2024届高二上学期开学检测数学试题浙江省宁波市三锋教研联盟2022-2023学年高一下学期期中联考数学试题(已下线)立体几何专题:立体几何探索性问题的8种考法(已下线)13.2.4 平面与平面的位置关系 (1)河北定州中学2022-2023学年高一下学期5月月考数学试题新疆阿克苏市实验中学2022-2023学年高一下学期第三次月考数学试题(已下线)8.5.3 平面与平面平行【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
名校
8 . 已知函数
.
(1)判断函数
的单调性,并证明;
(2)若
,记
,求证:
有且只有一个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c8a8af02118cf6f1fcbc437727e386.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7853903201ad06812c2aad48da23b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
您最近一年使用:0次
2023-02-18更新
|
181次组卷
|
3卷引用:江西省南昌市第五中学2022-2023学年高一下学期第一次(3月)月考数学试题
名校
解题方法
9 . 如图,在三棱柱
中,
底面
是
中点,
与
相交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/b9f59dbf-8be4-46d6-8f37-2fdfb8194af3.png?resizew=159)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
平面
;
(2)若四边形
是正方形,
,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd133a4014872dc424de7c4f5b0a7b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/b9f59dbf-8be4-46d6-8f37-2fdfb8194af3.png?resizew=159)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78f0b646ccbe31c8d4df21054f82003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a0c0eede7a2812304abae4e0e91738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
您最近一年使用:0次
2022-12-09更新
|
683次组卷
|
8卷引用:江西省新余市2023届高三上学期期末质量检测数学(文)试题
江西省新余市2023届高三上学期期末质量检测数学(文)试题陕西省榆林市神木中学2021-2022学年高一上学期第三次检测数学试题陕西省渭南市韩城市新蕾中学2021-2022学年高一上学期第三次月考数学试题(已下线)空间直线、平面的垂直(已下线)8.6.1 空间直线、平面的垂直(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.6.3平面与平面垂直(第1课时平面与平面垂直的判定定理)(精讲)(1)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)专题09 基本图形的平行与垂直-期中期末考点大串讲(苏教版2019必修第二册)(已下线)高一数学下学期期末模拟试卷01-【题型分类归纳】(苏教版2019必修第二册)
名校
解题方法
10 . 如图,在三棱柱
中,
是边长为4的正方形,平面
平面
,
,
,点
是
的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/a220b539-d15b-4fc6-9a79-067aec354190.png?resizew=134)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
平面
;
(2)求证:
平面
;
(3)证明:在线段
上存在点
,使得
.并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.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/editorImg/2022/12/7/a220b539-d15b-4fc6-9a79-067aec354190.png?resizew=134)
(1)求证:
![](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/ea55a7e39361987096953d3a3ee1eaa4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(3)证明:在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84a436704964dc76f16c2c23665ab3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04c68f1ef1e37534b5bbc7a1f592ef7.png)
您最近一年使用:0次
2022-12-04更新
|
709次组卷
|
2卷引用:江西省南昌市外国语学校2022-2023学年高二上学期期末考试数学试题