名校
解题方法
1 . 设函数
,
为
的导函数.
(Ⅰ)当
时,证明:
;
(Ⅱ)设
为函数
在区间
内的零点,其中
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139e79a0726b6cbb86966ff1d405b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b42048481d02f1112bbcd877790334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c52557b511fa214776612699697f39.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c2eda063d880d52576237aac880434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8e497f623891316aca634eb9c223d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72fd4ff7085ca173689e9306131733.png)
您最近一年使用:0次
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2 . 已知函数
.
(1)若曲线
在
处的切线与
轴平行,求
;
(2)已知
在
上的最大值不小于
,求
的取值范围;
(3)写出
所有可能的零点个数及相应的
的取值范围.(请直接写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8854951afdedd866aa87f3514d67e35b.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-12-04更新
|
631次组卷
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6卷引用:2020届北京市朝阳区六校高三四月联考数学(B卷)试题
名校
3 . 已知
,
.
(Ⅰ)若
在
恒成立,求实数a的取值范围;
(Ⅱ)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294ed75f9d437ffc32235bcb602365c.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141474ccc99264222f71b286b7a205b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c41acefa82be8127e9b338aa45b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0fb31594f2dc42bcc0a113cea5a560.png)
您最近一年使用:0次
2020-11-30更新
|
300次组卷
|
8卷引用:2020年1月中学生标准学术能力诊断性测试诊断性测试文科数学试卷
2020年1月中学生标准学术能力诊断性测试诊断性测试文科数学试卷2020届黑龙江省安达市第七中学高三下学期第一次网络检测数学(理)试卷中学生标准学术能力诊断性测试2019-2020学年高三1月(一卷)数学(文)试题2020年浙江省新高考名校交流模拟卷数学试题(二)陕西省西安市铁一中学2020-2021学年高三上学期第四次月考理科数学试题浙江省名校协作体2019-2020学年高三第一学期第一次联考数学试题(已下线)【新东方】杭州新东方高中数学试卷375(已下线)广东省佛山市第一中学2024届高三上学期第二次调研数学试题变式题17-22
名校
4 . 已知函数
.
(1)求函数
的极值;
(2)证明:当
时,曲线
恒在曲线
的下方;
(3)讨论函数
零点的个数.
参考公式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db43120cc632891762bf783201316f6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2eff609c6043c2a89a6dd163fe2244.png)
(3)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee7e0fba5abb4193f070f95fc5bbade.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a17290b3b75dfb2324e355cf2f3f4a.png)
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5 . 已知任意的正整数n都可唯一表示为
,其中
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92a109f29f48ad436c42ecf39e94bd5.png)
,
.对于
,数列
满足:当
中有偶数个1时,
;否则
,如数5可以唯一表示为
,则
.
(1)写出数列
的前8项;
(2)求证:数列
中连续为1的项不超过2项;
(3)记数列
的前n项和为
,求满足
的所有n的值.(结论不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ca3c160eb08349060a309726f75765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489340c9a2d70c00bae13b7018cad448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92a109f29f48ad436c42ecf39e94bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e13e7f28f377a019cb125bb5828da18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e784a7b36813c7cebe42bb8856ae4f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2023f7d7b5bdc3c7e0fc2a00debb3081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcb936b1197e44381d13b31dbfd8072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff90c2652820fd6d5740e67767f2348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2672e70cbf461aa960bfc38136a9f657.png)
(1)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe6857b99c7f80dd65b0ebfa6551674.png)
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2020高三·北京·专题练习
6 . 已知椭圆
的短轴长为2,离心率
,
(1)求椭圆
方程;
(2)若直线
与椭圆交于不同的两点
,与圆
相切于点
,
①证明:
(其中
为坐标原点);
②设
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c83f9e7f57d03304c3d0e51f43aa5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1595aacea3b417196e776cedbefdfca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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12-13高三下·北京海淀·期末
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7 . 设A是由
个实数组成的m行n列的数表,如果某一行(或某一列)各数之和为负数,则改变该行(或该列)中所有数的符号,称为一次“操作”.
(1)数表A如表1所示,若经过两次“操作”,使得到的数表每行的各数之和与每列的各数之和均为非负实数,请写出每次“操作”后所得的数表(写出一种方法即可):
表1
(2)数表A如表2所示,若必须经过两次“操作”,才可使得到的数表每行的各数之和与每列的各数之和均为非负整数,求整数 a的所有可能值:
表2
(3)对由
个实数组成的m行n列的任意一个数表A,能否经过有限次“操作”以后,使得到的数表每行的各数之和与每列的各数之和均为非负实数?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
(1)数表A如表1所示,若经过两次“操作”,使得到的数表每行的各数之和与每列的各数之和均为非负实数,请写出每次“操作”后所得的数表(写出一种方法即可):
1 | 2 | 3 | |
1 | 0 | 1 |
(2)数表A如表2所示,若必须经过两次“操作”,才可使得到的数表每行的各数之和与每列的各数之和均为非负整数,求
a | |||
(3)对由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
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2023-05-31更新
|
619次组卷
|
9卷引用:2013届北京市海淀区高三5月期末练习(二模)理科数学试卷
(已下线)2013届北京市海淀区高三5月期末练习(二模)理科数学试卷(已下线)2013届北京市海淀区高三5月期末练习(二模)文科数学试卷(已下线)2014届北京101中学高三上学期10月阶段性考试理科数学试卷北京市首都师范大学附属中学2023届高三下旬阶段性检测数学试题北京市第一六六中学2024届高三上学期10月阶段性诊断数学试题北京市牛栏山一中2024届高三下学期学期考前热身(三模)数学试题(已下线)专题01 条件开放型【练】【北京版】江西省鹰潭市2024届高三第一次模拟考试数学试题上海师范大学附属中学2022-2023学年高一下学期期末数学试题
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8 . 如图,已知椭圆
:
,直线
:
交椭圆
于
两点.过左焦点且斜率为
(
)的直线交椭圆
于
两点,线段
的中点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/3b96fe9b-b153-4a42-a377-b3db49cdfa9c.png?resizew=209)
(1)求椭圆
的离心率及实轴长;
(2)若点
在直线
上,试求
的关系式;
(3)在(2)的前提下,是否存在实数
,使得
的面积是
面积的6倍?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aca3272c91ba9773f1c8342cdfdc432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf4badc1b00534aefdc9508f8e6f636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/3b96fe9b-b153-4a42-a377-b3db49cdfa9c.png?resizew=209)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee956329e95a172d86c86b2f6af7aec.png)
(3)在(2)的前提下,是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df6d51738ac1bc8b9530ea4a55745c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b280088a8f97b52c2145bc709434e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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9 . 已知数列
的首项
其中
,
, 令集合
.
(1)若
,写出集合
中的所有的元素;
(2)若
,且数列
中恰好存在连续的7项构成等比数列,求
的所有可能取值构成的集合;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48de213e934c8956ebd457d02e9082b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138e3b3232967d256fb4ec758ed9730e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fd42571d62a4415616c6c2b5f59b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e2d7b157d84529fb8e7826fecdeadc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583d2d3270e143e544b82af6027acc66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
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解题方法
10 . 已知三次函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若函数
在区间
上具有单调性,求
的取值范围;
(3)当
时,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b999729b246f46e24a1d051237bfd9ae.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b13280d106fe9c3db2069984325b63.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3657d20b49b421286049b1bf11b819f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d58b0e00d782782712e3ba9076ad8f3.png)
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2020-11-15更新
|
1187次组卷
|
5卷引用:北京市海淀区2021届高三上学期期中考数学试题
北京市海淀区2021届高三上学期期中考数学试题北京市北大附属实验学校2022届高三上学期期中考试数学试题北京市第四十三中学2022届高三上学期期中考试数学试题北京市北京师范大学附属实验中学2022届高三上学期期中考试数学试题(已下线)单元卷 导数及其应用(提高卷)-2020-2021学年高二数学课时同步练(苏教版选修1-1)