1 . 对于任意的实数
,总存在三个不同的实数y,使得
成立,其中e为自然对数的底数,则实数a的取值范围是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3178c8f2f812d05b4d622c159f5a7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
2 . 已知函数
,若集合
中恰有3个元素,且它们的和为0,则实数
的取值集合是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71bc86fb6f75a5f34df5b07813b5c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2695b714512a3bf00459ed35bd5ebd22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2023-12-01更新
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3卷引用:天津市南开中学2023-2024学年高一上学期第二次学情调查数学试题
名校
3 . 已知函数
,若函数
与
的图象恰有5个不同公共点,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a74d88c4d841156e04411eeae3d30a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a448aee939c98ef0044362e52d14b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6e318aeb4f2bfa58d289dbaedf91a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4卷引用:天津市咸水沽第一中学2023-2024学年高三上学期期中考试数学试题
名校
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0ebc77b83210330497b573b39c458e.png)
(1)当
时,求
在点
处的切线方程;
(2)若
对
恒成立,求实数
的取值范围
(3)
若有3个零点
,其中
,求实数
的取值范围,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0ebc77b83210330497b573b39c458e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b13280d106fe9c3db2069984325b63.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e728e7423960080153f3ef30e2b708d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5daf486cf2adbd7af8aa26fe66b57ce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c06068ac2d0da29abec54df3f84347.png)
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2卷引用:天津市第一百中学2023-2024学年高三上学期期中数学试题
5 . 已知椭圆:
:
的离心率
,连接椭圆的四个顶点得到的菱形的面积为
.
,
是椭圆
的两个焦点.
(1)求椭圆
的方程;
(2)设
为E的左顶点,过
点作两条互相垂直的直线
分别与E交于
,
两点,证明:直线
经过定点,并求这个定点的坐标.
(3)设
是椭圆
上一点,直线
与椭圆
交于另一点
,点
满足:
轴且
,求证:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97bde5efa645a4c1ed6874088400d6a7.png)
![](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/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2784a52c4da98dc9df661fc152fc29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d6de923fac9e8a6bccfb8e2b68a4bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57abf0dc1e0bf1a11dbef810607de18.png)
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6 . 已知函数
.
(1)当
时,求曲线
在
处切线的斜率;
(2)讨论函数
的单调性;
(3)若
有两个极值点
,且
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97227e82a644fdaa750975fbab2be46f.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/707ea658f3a9359f5740d5aab48f7948.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98919b1335a8b7ca020636d1494ad0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a844b9c0d7ea04428d8ba115709d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . 已知函数
.
(1)若曲线
在
处的切线斜率为1,求a的值;
(2)讨论
的零点个数;
(3)若
时,不等式
恒成立,求a的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c23cae58b1b3a67d442713e79b0b15.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000c8eeee025a5abf590f614e17c7891.png)
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8 . 已知动点
在抛物线
上,过点
引圆
的切线,切点分别为
,
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da2419d703e4494762087407752e9865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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4卷引用:天津市第四十七中学2023-2024学年高二上学期11月期中数学试题
名校
9 . 已知函数
,
(1)当
时,求函数
在
处的切线方程;
(2)讨论函数
的单调性;
(3)当函数
有两个极值点
且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5facb7583ea00e6d8db952d80557f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.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/9b384412acba251d87902ab928902f16.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b314f6ccb0a3e4fc15685d85e55bf6.png)
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14卷引用:天津市五区县重点校2022-2023学年高二下学期期中联考数学试题
天津市五区县重点校2022-2023学年高二下学期期中联考数学试题广东省梅州市东山中学2022届高三上学期期中数学试题天津市第五十五中学2021-2022学年高三上学期10月学情调研数学试题云南衡水实验中学2022届高三上学期期中考试数学(理)试题天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷2福建省宁化第一中学2022届高三9月第二次月考数学试题黑龙江省哈尔滨工业大学附属中学校2021-2022学年高二上学期期末考试数学(理)试题(已下线)2020年高考天津数学高考真题变式题16-20题(已下线)第13讲 双变量问题-2022年新高考数学二轮专题突破精练河南省洛阳市洛宁县第一高级中学2022-2023学年高二下学期2月月考数学理科试题江苏省南京大学附属中学2022-2023学年高二下学期3月月考数学试题广西壮族自治区梧州市苍梧中学2022-2023学年高二下学期3月月考数学试题(已下线)模块五 专题5 期中重组卷(广东)(已下线)导数专题:导数与不等式成立问题(6大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)
名校
解题方法
10 . 已知函数
.
(1)令
,讨论
的单调性并求极值;
(2)令
,若
有两个零点;
(i)求a的取值范围:
(ii)若方程
有两个实根
,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca646a9f0e0060891a82c39e33dd6af.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bb9e98b6699fbfed3772d75c6bbe46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155064e0bec1198c32041d1daf82e678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(i)求a的取值范围:
(ii)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1b97fbb2cf9a6b3d290e921d8a9a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6677f8f96f7982de5637c229a49e4b37.png)
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10卷引用:天津市第二南开学校2021-2022学年高三上学期期中数学试题
天津市第二南开学校2021-2022学年高三上学期期中数学试题天津市实验中学滨海学校2022-2023学年高二下学期期中数学试题天津市滨海七校2020-2021学年高三上学期期末联考数学试题天津市耀华中学2022届高三下学期统练9数学试题天津市北京师范大学天津附属中学2022-2023学年高三上学期期末数学试题四川省绵阳南山中学2022-2023学年高三上学期绵阳一诊热身考试理科数学试题黑龙江省哈尔滨市第九中学校2022-2023学年高三上学期第三次月考数学试题(已下线)第二篇 函数与导数 专题6 函数周期性、对称性、拐点 微点2 函数的拐点与对称中心(已下线)模块八 专题11 以函数与导数为背景的压轴解答题(已下线)北京市丰台区2023届高三下学期3月一模数学试题变式题16-21