真题
1 . 若函数
恰有一个零点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed0abc69199027468e3c0216acc74c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7日内更新
|
1949次组卷
|
5卷引用:2024年天津高考数学真题
名校
解题方法
2 . 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)
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名校
解题方法
3 . 已知椭圆
左右焦点为
,
,A是上顶点,B是右顶点,
.
(1)求椭圆的离心率;
(2)当
时,直线l与椭圆相切于第二象限的点D,与y轴正半轴相交于点M,直线AB与直线l相交于点H,
为H在x轴上投影,若
(
表示
的面积,O为坐标原点),求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f669879b41f5340ec51ada9b1b5effb.png)
(1)求椭圆的离心率;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f5c4d08d4fae3e36b6404a777292d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d955d197e2ecbfe724570663efcf2a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7220826b356cf233b21ae09ac4edf174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c6296f0e3b67fa020788b37697304b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f3d2eeda1aca7ea401038aaecf2240.png)
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名校
4 . 已知
,函数
,
.
(1)若函数
的最小值是0,求实数m的值;
(2)已知曲线
在点
处切线的纵截距为正数.
(ⅰ)证明:函数
恰有两个零点;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a68e9852ea3d8e348d284d6df9ca68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a25dcb67d1cb242a60f4fb8f3468a1.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(ⅰ)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc250d99a55c62b89da6ad253978515.png)
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5 . 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)
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名校
6 . 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)
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2024-04-24更新
|
924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)
名校
解题方法
7 . 已知数列
满足对任意的
,均有
,且
,
,数列
为等差数列,且满足
,
.
(1)求
,
的通项公式;
(2)设集合
,记
为集合
中的元素个数.
①设
,求
的前
项和
;
②求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6cbbec0f900da8864d00e396893c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e506112c35bdf08b18460d233eb6595.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bc4ebb7c9c2323c75011db21226ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc96f796c19909fe80d0da1cd1d7823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b255b2aa8a99d13c0756a87906675c7f.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac6b8de4384ff605892e8de5263de13.png)
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名校
解题方法
8 . 已知椭圆
的左右顶点为A,B,上顶点与两焦点构成等边三角形,右焦点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
(1)求椭圆的标准方程;
(2)过
作斜率为
的直线
与椭圆交于点
,过
作l的平行线与椭圆交于P,Q两点,与线段BM交于点
,若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
(1)求椭圆的标准方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57765e1727023ffa9686979482722f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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9 . 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)
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2024-04-17更新
|
1405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
解题方法
10 . 已知函数
(
),
.
(1)求函数的极值;
(2)若
对任意的
恒成立,求实数
的取值范围;
(3)求证:
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0efa793fc95d2bbcc8eec1d375343f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c9e984f50dac827078864092aa9a7bc.png)
(1)求函数的极值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5822ea5f9009e579f59f011db39196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5816f5a4a74bbf091588680f9885b829.png)
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