名校
解题方法
1 . 已知函数
,其中
为实数.
(1)当
时,
①求函数
的图象在
(
为自然对数的底数)处的切线方程;
②若对任意的
,均有
,则称
为
在区间
上的下界函数,
为
在区间
上的上界函数.若
,且
为
在
上的下界函数,求实数
的取值范围.
(2)当
时,若
,
,且
,设
,
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4d96931977f6f5462acb196bcd417e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea4d74f476f741b75a448ee01c0e86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f121036d30c000b01b7be98d9c8a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f121036d30c000b01b7be98d9c8a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e75907a1b513cdf63614b4b68ece89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb0aa7bf71da74a9b3d4a022812290a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f861459b5e5a3ce298f205d9677e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd34bc2979bfed0fa99269635dde578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9499b9c4b5292d3f28799d1e96653ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253fe46f6392ea2a63475453fbe5b16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cce18618decec25cc47f40f2f7478f.png)
您最近一年使用:0次
7日内更新
|
57次组卷
|
2卷引用:天津市滨海新区2023-2024学年高三第三次模拟考试数学试卷
2 . 已知函数
若函数
(
)(
为自然对数的底数)恰有4个零点,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb4e3b94f9d57e0a137fcb770f3e5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57a713236f811d406014d1b9d7d1092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)求
在点
处的切线方程;
(2)若
恒成立,求
的值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b086b1659a2d49b8e0b4239a353bc146.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3b52d1c073c1fda251dcc0b51fb41d.png)
您最近一年使用:0次
4 . 已知函数
.
(1)求函数
的单调区间;
(2)若函数
在
处取得极大值,求实数
的取值范围:
(3)已知
,曲线
在不同的三点
处的切线都经过点
,且
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50bdf9cc570f3ad7245aca7087abe6b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a54f63ff36b084047321e09cbcee442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606ef9cb8c9c4f61ab2acc4c11fec693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5149c72ec2f361d9220b6bf8bba4dc3.png)
您最近一年使用:0次
名校
5 . 设
,函数
,若函数
恰有4个零点,则实数
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e37c35e33ffa1a55a0693ae2319da91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627cd24f63d5c5987cb718e6eddfe6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a576992d969ed5d63a8f77af2c7edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-04-24更新
|
948次组卷
|
4卷引用:天津市八校2023-2024学年高三下学期联合模拟考试数学试题(二)
天津市八校2023-2024学年高三下学期联合模拟考试数学试题(二)天津市第四十七中学2023-2024学年高二下学期第二次阶段性检测(6月)数学试题(已下线)第25题 函数方程是“近亲”,以形助数传“佳话”(优质好题一题多解)(已下线)专题6 函数的零点问题(过关集训)(压轴题大全)
6 . 已知集合
,定义:当
时,把集合
中所有的数从小到大排列成数列
,数列
的前
项和为
.例如:
时,
,
.
(1)写出
,并求
;
(2)判断88是否为数列
中的项.若是,求出是第几项;若不是,请说明理由;
(3)若2024是数列
中的某一项
,求
及
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc6c83969f0c67473049709952b50e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d47710bdf547780bc9c29c42423cce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b33a624f32310f1ef43686ea593ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b33a624f32310f1ef43686ea593ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bd390fa43014ff48549a6ca941d38c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2046390ed7657e860458b026a4ced115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ac0dba37b8eb22670b24c350af0b54.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ae09a97dd40d6b317a448664bf3816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5f4584826926dbc15fae9fb75d36ec.png)
(2)判断88是否为数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59038077a6db85e9b790b14eecf717a.png)
(3)若2024是数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b33a624f32310f1ef43686ea593ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1180a64221e78248cb691ecc21ec18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e05ea594b5b86bcbbad940b46000f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9c79f3f90e6ed44e479b2e4ff16f05.png)
您最近一年使用:0次
2024-04-17更新
|
1418次组卷
|
5卷引用:天津市南开中学2024届高三下学期模拟检测数学试题
天津市南开中学2024届高三下学期模拟检测数学试题2024届浙江省嘉兴市二模数学试题(已下线)第四套 艺体生新高考全真模拟 (二模重组卷)(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总(已下线)压轴题01集合新定义、函数与导数13题型汇总-2
名校
7 . 已知函数
.
(1)如果1和
是
的两个极值点,且
的极大值为3,求
的极小值;
(2)当
时,讨论
的单调性;
(3)当
时,且函数
在区间
上最大值为2,最小值为
.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae06c488100e31570805778b1d322e4.png)
(1)如果1和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347bb4ffedcbea2f4c16d047a138d75.png)
您最近一年使用:0次
2024-03-31更新
|
1839次组卷
|
5卷引用:天津市南开中学2024届高三下学期模拟检测数学试题
天津市南开中学2024届高三下学期模拟检测数学试题浙江省9+1联盟2023-2024学年高三下学期3月高考模拟数学试卷(已下线)模块3 第4套 全真模拟篇(一模重组卷)(已下线)专题1 导数与函数的单调性(恒单调、存在单调区间、不单调)【练】(已下线)专题2 导数与函数的极值、最值【练】
解题方法
8 . 意大利画家达
芬奇提出:固定项链的两端,使其在重力的作用下自然下垂,那么项链所形成的曲线是什么?这就是著名的“悬链线问题”,通过适当建立坐标系,悬链线可为双曲余弦函数
的图象,定义双曲正弦函数
,类比三角函数的性质可得双曲正弦函数和双曲余弦函数有如下性质①平方关系:
,②倍元关系:
.
(1)求曲线
在
处的切线斜率;
(2)若对任意
,都有
恒成立,求实数
的取值范围:
(3)(i)证明:当
时,
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed02acb0c7b4e40c26f6760627a033e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbcc2e6bbcbd9344009a0b032a42fbeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6365b6a2c34ad432c87a18f5ff9a9753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14b6e2c6388fab46c84ba19b6fde908.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1ee2c2965ab4a51d26062fb0e665a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a0f5d601c1a7fff1e48cab44f2006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)(i)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95404c4329755d2cfe49c8ca6861d240.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9363fed5ed3715f9a94fa52e59cea9f7.png)
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9 . 已知函数
有且仅有2个零点,则实数
的取值范围为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48346b3c731bac4c0a5fee9fee437d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
10 . 设函数
.
(1)求曲线
在点
处的切线方程;
(2)设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9810e3429cbc74154fcd120f36f522aa.png)
(i)当
时,
取得极值,求
的单调区间;
(ii)若
存在两个极值点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71449033e39f2f7cc622987f267d3df6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9810e3429cbc74154fcd120f36f522aa.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd83f16ea130e2f7c33a09b75987ca36.png)
您最近一年使用:0次