名校
1 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若
时,
,求a的取值范围;
(3)对于任意
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27862c9517dbb4eb17a6725eb142969.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af027bd16e380d3be03a9761ca56055.png)
您最近一年使用:0次
2024-01-18更新
|
2008次组卷
|
9卷引用:四川省成都市第七中学2024届高三上学期期末数学(理)试题
名校
解题方法
2 . 已知函数
(其中
为实数).
(1)若
,证明:
;
(2)探究
在
上的极值点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a57451cb33cee6a4876b5602c700f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfbd4a8f720eb187ecfd4b4fe69d1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28933f93d4952657848a1564f37bd6e5.png)
您最近一年使用:0次
2024-01-03更新
|
928次组卷
|
8卷引用:四川省广安市2024届高三一模数学(理)试题
名校
解题方法
3 . 设函数
,
.
(1)①当
时,证明:
;
②当
时,求
的值域;
(2)若数列
满足
,
,
,证明:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df075cd20f79486d88d80ee12fc897d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5883f63cdc68865d41cc935b7b39557d.png)
(1)①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffa28c7f519c1c85c0a3cad23b2e6cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ebb32ddcd84417fc992dad3ccba8894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adfbda63ad7cfeb044819141f1924598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
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2023-12-30更新
|
1078次组卷
|
4卷引用:四川省成都市第七中学2024届高三上学期期末数学(理)试题
(已下线)四川省成都市第七中学2024届高三上学期期末数学(理)试题重庆市育才中学、万州高级中学及西南大学附中2024届高三上学期12月三校联考数学试题广东省广州市华南师大附中2024届高三上学期大湾区数学预测卷(一)(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
4 . 设函数
,
,其中e是自然对数的底数.
(1)若曲线
在
处的切线与曲线
相切,求a的值;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4f7cd2e4835c2d3de36a3d74fbd2cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e1ebf726424e476f2ebf169381381e.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e9dd2104e1732ea13fe10c207eb3fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9039b184aba70f205175639b4cdc66c7.png)
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2023-07-13更新
|
242次组卷
|
2卷引用:四川省泸州市2022-2023学年高二下学期期末数学理科试题
名校
5 . 如图,在四棱锥
中,
,
,
,△MAD为等边三角形,平面
平面ABCD,点N在棱MD上,直线
平面ACN.
.
(2)设二面角
的平面角为
,直线CN与平面ABCD所成的角为
,若
的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e05d8681a679bd31922e62480f69d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451604e8cbe0706585d9cd2c76db4b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74c46a80f7540470b5e171e2e17d3bf.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698335f4880c7a298f4898c83b6562bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de9d1a07d32cae0e86d73482477da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2023-06-30更新
|
2882次组卷
|
8卷引用:四川省2022-2023学年高一下学期“贡嘎杯”期末质量检测考试数学试题
名校
6 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)设函数
,当
时,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fe84ecdcafb66c2e3a4dd702503729.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effd486acb416eb05e02a19727227bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe40d74887c7473b2ff4d56ffac22ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a415767156945ea8ada9ed3756019fc.png)
您最近一年使用:0次
2023-02-26更新
|
836次组卷
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3卷引用:四川省成都市蓉城联盟2022-2023学年高三下学期第二次联考文科数学试题
四川省成都市蓉城联盟2022-2023学年高三下学期第二次联考文科数学试题四川省绵阳市绵阳中学2024届高三下学期三诊模拟考试数学(理)试题(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点3 利用导数证明含三角函数的不等式(三)
名校
7 . 已知函数
.
(1)若
,
,求实数a的取值范围;
(2)设
是函数
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cc71eacaec8e1aaeffec91d19518fa.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc1d8bb31485daaab989fb4368db6eb.png)
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2023-03-29更新
|
2894次组卷
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8卷引用:四川省宜宾市第六中学校2024届高三上学期期末数学(理)试题
四川省宜宾市第六中学校2024届高三上学期期末数学(理)试题江苏省南京市金陵中学2022-2023学年高二下学期期末数学试题江苏省八市(南通、泰州、扬州、徐州、淮安、连云港、宿迁、盐城)2023届高三二模数学试题(已下线)押新高考第22题 导数综合解答题(已下线)江苏省八市2023届高三二模数学试题变式题17-22专题07导数及其应用(解答题)浙江省宁波市余姚中学2023-2024学年高二上学期第一次质量检测数学试题江苏省八市2023届高三下学期第二次调研测试数学试题
8 . 已知椭圆
的右焦点为
,若过点
的直线与椭圆交于
两点,且
的中点为
.
(1)求椭圆
的方程;
(2)若椭圆
的右顶点为
,点
在椭圆
上,且满足直线
与
的斜率之积为
,证明:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ce47fde921058026708a4321a0e213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc72e9470cdf9d24a77ab451c9348e8d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8930e9a26a52a6b09740c1dddbd40e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,斜三棱柱
中,
,
为
的中点,
为
的中点,平面
⊥平面
.
平面
;
(2)设直线
与直线
的交点为点
,若三角形
是等边三角形且边长为2,侧棱
,且异面直线
与
互相垂直,求异面直线
与
所成角;
(3)若
,在三棱柱
内放置两个半径相等的球,使这两个球相切,且每个球都与三棱柱的三个侧面及一个底面相切.求三棱柱
的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1638cde11c9862af200115048a0177da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53cdc56590b42b154608b4cf19462fa0.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e190568dc620895856a72fca1a08ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770da0f9a22d31e40431208bb33ab8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
2022-11-29更新
|
3493次组卷
|
7卷引用:四川省成都市2022-2023学年高一下学期期末数学试题
名校
解题方法
10 . 已知在
中,
.证明:
(1)
;
(2)
在
上恒成立;
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92a98e220a9a1f2a1caa37e4cf4e213.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5e4691210486a560c59df09937d9f8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991a6e773c41687e5b13d36da7612e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb222ce13688da6fc57089ebf5812b0e.png)
您最近一年使用:0次