名校
解题方法
1 . 已知函数
,
.
(1)当
时,直线
与
相切于点
,
①求
的极值,并写出直线
的方程;
②若对任意的
都有
,
,求
的最大值;
(2)若函数
有且只有两个不同的零点
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bad889fec9bf544f9b3284fe15bc7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc0290845bd3245644c6d22485d9e8c.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3ea46bcfd4d1ade2e65f8b28b7f7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259668a667eca172a19a99229c9fbc3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933436a516df078f4c4250d698310c13.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/d3661dbd3b2c578c685e6a11a4102ddd.png)
您最近一年使用:0次
2021-04-03更新
|
1539次组卷
|
8卷引用:天津市宝坻区第一中学2021届高三下学期二模数学试题
天津市宝坻区第一中学2021届高三下学期二模数学试题天津市和平区2021届高三下学期一模数学试题(已下线)天津市和平区2021届高三下学期第一次质量调查数学试题(已下线)押第21题 导数的应用-备战2021年高考数学(文)临考题号押题(全国卷2)(已下线)专题2.13 导数-零点问题-2021年高考数学解答题挑战满分专项训练(新高考地区专用)江苏省泰州市泰兴市第一高级中学2022届高三下学期阶段测试二数学试题江西省九江市德安县第一中学2022-2023学年高二下学期7月期末数学试题(已下线)专题02 一元函数的导数及其应用(7大题型+优选提升)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)
名校
解题方法
2 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆
的标准方程;
(2)点
是椭圆
与
轴正半轴的交点,点
,
在椭圆
上且不同于点
,若直线
、
的斜率分别是
、
,且
,试判断直线
是否过定点,若过定点,求出定点坐标,若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef404abca1f78da130a38849f58559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97d3cf0f550e8f9e1da0f645201b731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6f62ec9c0e58b3f1c363158269b14d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ff131c92aa9e10f696d374216cdcf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ef1ccb69abec8bfaaee4ed3f140dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2020-12-02更新
|
1929次组卷
|
6卷引用:天津市宝坻区第一中学2021届高三下学期二模数学试题
天津市宝坻区第一中学2021届高三下学期二模数学试题天津市市区重点中学2023届高三下学期一模数学试题河南省豫南九校2020-2021学年第一学期高二第三次联考(11月)理数试题天津市静海区第一中学2020-2021学年高三上学期期末数学试题(已下线)黄金卷02-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)豫南九校2022-2023学年高二上学期第三次联考数(理)试题
名校
3 . 已知函数
,若函数
恰有三个零点,则实数
的取值范围为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f90e1afe802231da30bae9e7b1afc6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fd0cd26a9a38588a0311c39708d186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-08-19更新
|
1672次组卷
|
7卷引用:天津市宝坻区大口屯高级中学2021届高考模拟数学试题
20-21高二下·浙江·期末
解题方法
4 . 设等差数列
的公差为d,d为整数,前n项和为
,等比数列
的公比为q,已知
.
(1)求数列
与
的通项公式;
(2)求数列
的前n项和为
;
(3)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babd3af8d92d9af9d1560606f71e064b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda289a8fdf0b1bc96bcca6b878764c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f95ce9d509a67c963d8b6d8c33e04b.png)
您最近一年使用:0次
名校
5 . 如图,在等腰三角形
中,已知
,
分别是
上的点,且
,
(其中
,
),且
,若线段
的中点分别为
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63024bdfefbb725b0629315ec925b48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47e63cc9c18c7a6c356748534993f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf88849d6d46dcab690608ab9e5d7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558f134032cd487914aef62fe1b7d208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d6ff84712e33efb6140658e816e548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c877203215bd4cdc93dd0a6cb66f551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b405c36bca1dca1aa0483386c8fc62b3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/c9eb9e0b-5d4d-453e-8562-b8cdad1ba362.png?resizew=177)
您最近一年使用:0次
2019-05-08更新
|
1961次组卷
|
3卷引用:天津市宝坻区第一中学2022届高三下学期二模数学试题
名校
6 . 已知函数
.
(Ⅰ)当
时,求
在点
处的切线方程;
(Ⅱ)若
,求函数
的单调区间;
(Ⅲ)若对任意的
,
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7690530f7dd6a7e234a0f0661e2698.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c46d700808f2cc9e9059d0944afd94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅲ)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230c810b0a1c851ec85a2913ad153752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b916c6d3fb2fdc67421489f207c93903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2019-05-03更新
|
1478次组卷
|
5卷引用:天津市宝坻区大口屯高级中学2021届高考模拟数学试题
天津市宝坻区大口屯高级中学2021届高考模拟数学试题【校级联考】天津市十二重点中学2019届高三下学期毕业班联考(二)数学(理)试题江苏省盐城中学2019-2020学年高二下学期期中数学试题天津市北辰区华辰学校2021-2022学年高三上学期第二次月考数学试题(已下线)第14讲 端点恒成立与端点不成立问题-2022年新高考数学二轮专题突破精练
真题
名校
7 . 设等差数列
的前
项和为
,且
,
.
(Ⅰ)求数列
的通项公式;
(Ⅱ)设数列
的前
项和为
,且
(
为常数),令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d6c09b07bbac3de53f81c07d1e2e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bcf28f6f65d41f1ea14c7ba8d7f5d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde13a1d82174255f34cc22f8127787b.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(Ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3b65cdb9616f516a155c1dff6d29a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4c7da604269ba263e652ad717d8034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a2d454cd9842cc890b8b0b9fca8a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f1ebca4cf1a783942797f6f1ad97d0.png)
您最近一年使用:0次
2016-12-02更新
|
2536次组卷
|
3卷引用:天津市宝坻区第一中学2019届高三三模理科数学试题
名校
8 . 若函数
,有三个不同的零点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340a4678c041569f559add16d5650bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45ea1d522a3ebbf5f5d8d330fdbd1e6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-04-25更新
|
1030次组卷
|
5卷引用:天津市宝坻区第一中学2019届高三三模理科数学试题
天津市宝坻区第一中学2019届高三三模理科数学试题【省级联考】新疆2019届高三第三次诊断性测试数学(理)试题天津市静海区第一中学2020届高三3月学生学业能力调研考试数学试题天津市南开中学滨海生态城学校2019-2020学年高二下学期期中数学试题(已下线)专题11 函数的零点-2020年高考数学母题题源解密(天津专版)
名校
解题方法
9 . 已知函数
(
为自然对数的底数).
(1)求函数
的单调区间;
(2)当
时,若
对任意的
恒成立,求实数
的值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14dee98f762932a2b717636a20306b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a90b936a01686cc776e994a1a69b5dc.png)
您最近一年使用:0次
2016-12-02更新
|
1475次组卷
|
6卷引用:天津市宝坻区第一中学2019届高三三模理科数学试题