2024高三上·全国·专题练习
名校
解题方法
1 . 已知
,
,
(1)若
在
处取得极值,试求
的值和
的单调增区间;
(2)如图所示,若函数
的图象在
连续光滑,试猜想拉格朗日中值定理:即一定存在
,使得
,利用这条性质证明:函数
图象上任意两点的连线斜率不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c566b6273b93a7231f891a0889579227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d60df31661ec394cdec5f0ad6bac38.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0843a602fe240e5798bcbc7d54b19ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)如图所示,若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7fc0ca8a82663b87fa36afb9c4ec09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3fcc5073759c73c7a63c8818eca5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a947d16d7293baf95e9274b9a0f5db78.png)
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2 . 已知多项式
.
(1)若
,且
有三个正实数根
,
,
,证明:
;
(2)对一般的正整数
,若
,
,
,
,证明:方程
的根不全是正实数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d310b3ca60508199bb95f15860232f4d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8de1c943439d47ca9e9a02e558a1b2e.png)
(2)对一般的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9772498c845b2043b375d1e8d8416b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e506a31a62c9581edb62218fce59b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f13c73c7894077a19b6c403587de96a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4e01e8ef5adf43e1f21591adbc3851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
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名校
解题方法
3 . 已知在
中,
.证明:
(1)
;
(2)
在
上恒成立;
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92a98e220a9a1f2a1caa37e4cf4e213.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5e4691210486a560c59df09937d9f8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991a6e773c41687e5b13d36da7612e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb222ce13688da6fc57089ebf5812b0e.png)
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名校
4 . 已知
,函数
,其中
…为自然对数的底数.
(1)证明:函数
在
上有唯一零点;
(2)记
为函数
在
上的零点,证明:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3adb9acead48e36b705874dc96979f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597de8046b5baecf54be4b0516de67ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89e13ea43300cc01379c96614d8e9cc.png)
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2021-10-12更新
|
558次组卷
|
3卷引用:湖北省武汉市部分重点中学2021-2022学年高二下学期期末联考数学试题
5 . 如图所示,设k>0且k≠1,直线l:y=kx+1与l1:y=k1x+1关于直线y=x+1对称,直线l与l1分别交椭圆
于点A、M和A、N.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/de2a14e9-1b7a-4097-971d-d543239d8a57.png?resizew=166)
(1)求
的值;
(2)求证:对任意的实数k,直线MN恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8868e2ba4401d727f1bcb1f5483b48f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/de2a14e9-1b7a-4097-971d-d543239d8a57.png?resizew=166)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec01614eda195be40a7d5fd494f7f344.png)
(2)求证:对任意的实数k,直线MN恒过定点.
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2020-05-11更新
|
618次组卷
|
2卷引用:辽宁省大连市部分学校2023-2024学年高二上学期期末考试数学试卷
6 . 已知集合
,且
中的元素个数
大于等于5.若集合
中存在四个不同的元素
,使得
,则称集合
是“关联的”,并称集合
是集合
的“关联子集”;若集合
不存在“关联子集”,则称集合
是“独立的”.
分别判断集合
和集合
是“关联的”还是“独立的”?若是“关联的”,写出其所有 的关联子集;
已知集合
是“关联的”,且任取集合
,总存在
的关联子集
,使得
.若
,求证:
是等差数列;
集合
是“独立的”,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cdcb0e77b3ae3e701c6b51e15e2346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeda5cef4846ef829069fe27f64e34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bf4032eb5a9ba68131b15182aa3491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9859aa908844a32c0e1e069a046727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918f1c94368c3a41177ff42cfedc0eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e0ad51c5541ec3dcca4a9845f8b7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498f92bf2e605cdbc91973e29b047566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4d89801d24aa43f47d6a366aad0571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ccce8225324817b0577551956464f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874781ab5711bff6ee8c9cbad5b3b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8021f4f4c253a00360bf8f9425610e1.png)
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2020-02-09更新
|
1565次组卷
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10卷引用:北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题
北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题北京市第五十七中学2021-2022学年高二下学期期末考试数学试题北京市日坛中学2023-2024学年高二下学期第三次月考(6月)数学试卷2020届北京市海淀区高三上学期期中数学试题(已下线)专题02 拿高分题目强化卷(第三篇)-备战2021年新高考数学分层强化训练(北京专版)北京市海淀区2021届高三模拟试题(一)(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮北京市第八中学2023届高三上学期12月测试数学试题上海市上海中学2022届高三下学期高考模拟3数学试题北京市朝阳区中国人民大学朝阳分校2021-2022学年高三上学期开学考数学试题
7 . 已知
,给定
个整点
,其中
.
(Ⅰ)当
时,从上面的
个整点中任取两个不同的整点
,求
的所有可能值;
(Ⅱ)从上面
个整点中任取
个不同的整点,
.
(i)证明:存在互不相同的四个整点
,满足
,
;
(ii)证明:存在互不相同的四个整点
,满足
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93cadf0f6a7b056d60ecb318674282f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b7c34c973fd0919fd96e15c3f6c2a0.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c175af9f46a65c426f9adccb676440b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52907dcc0fbee96a0f7f541b8d813b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973d9fbcf63adf3df6e633f08d12d678.png)
(Ⅱ)从上面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa74d66e7106b16a42279f8c7f55f4a.png)
(i)证明:存在互不相同的四个整点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699c0392b28bbfb75f61cea928760b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d767450e72edc9a8ae9d617f0f00573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c064e9b771463687b82b4d482c87b825.png)
(ii)证明:存在互不相同的四个整点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41156b089353814c1e11f6f7cca89e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a991faf6ceda2eafd0acd7e32aca89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6f3a6c1002546a7568c91ad97e47d8.png)
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2020-01-21更新
|
482次组卷
|
4卷引用:北京市中关村中学2020-2021学年高二上学期期中考试数学试题
名校
解题方法
8 . 已知函数
在
处的切线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ec60c1d5e99c7dd9d343f0127bff95.png)
(1).求
的解析式;
(2).若对任意的
,均有
求实数k的范围;
(3).设
为两个正数,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f89d1045355084403aa3c3bfe812a4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ec60c1d5e99c7dd9d343f0127bff95.png)
(1).求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2).若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147ed879fbe216a902b729fcbe96b981.png)
(3).设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36af67dca04ff106d65a4a3505acb224.png)
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