名校
解题方法
1 . 帕德近似是法国数学家亨利
帕德发明的用有理多项式近似特定函数的方法.给定两个正整数
,
,函数
在
处的
阶帕德近似定义为:
,且满足:
,
,
,
,
,注:
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
已知函数
.
(1)求函数
在
处的
阶帕德近似
,并求
的近似数
精确到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e2a6b3944261bb5b2e0244d05af639.png)
(2)在(1)的条件下:
①求证:
;
②若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16563cfb206d0394cac2a0c2595dda6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcb8c6a69df1a0deaba265e204d5f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a8c1ed551fccee1c1848746c5f282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72029562177dfc99a171c9013eb90227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4573475f70860a3d99b92a329d0d07f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca214aa6276b96d67a451c3fdbc59b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba6d8d56270fc72edd1af793542c036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030c5fc27fb5c07e4d6c913653af07ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f8f07548edb2d114804fbfca1eee55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5c1ae8ac7a70fcab9a5daca65ccd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e2a6b3944261bb5b2e0244d05af639.png)
(2)在(1)的条件下:
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec667cb20a6d670c47adfca4e4f5dd5.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad7d4b49b53e6d1aae16e515cf0975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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|
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7卷引用:山东省菏泽第一中学人民路校区2024届高三下学期3月月考数学试题
山东省菏泽第一中学人民路校区2024届高三下学期3月月考数学试题(已下线)模块3 第8套 全真模拟篇安徽省黄山市2024届高中毕业班第二次质量检测数学试题重庆市万州第二高级中学2023-2024学年高二下学期期中质量监测数学试题(已下线)专题12 帕德逼近与不等式证明【练】天津市武清区杨村第一中学2024届高考数学热身训练卷河北省秦皇岛市部分示范高中2024届高三下学期三模数学试卷
名校
2 . 已知函数
.
(1)当
时,判断
的单调性;
(2)若
存在两个极值点
,
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c01d5f28048dc4ef0d7b5fc68d34c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf785616045d41f62917779d91d4976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/f1f371db74b12dd32aadebfa05db729c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c233482fd5c64cebc0b14943efa2ee.png)
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名校
解题方法
3 . 已知函数
有两个不同的极值点
.
(1)求
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bad248263e288527d2974a80855906e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609b041d6bab322474ac57d9f1e91660.png)
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2024-04-07更新
|
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3卷引用:山东省大联考2023-2024学年高二下学期3月质量检测联合调考数学试题
名校
4 . 已知函数
,
,
为常数.
(1)求
的单调性;
(2)令
,若
且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2399c2a712a2890dcd0b195d3b9f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccea4fc613ed248eccae643ff009fcbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbb660534ebec95b0195fe34be3939b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047924127385f58348d477b18295d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b050ed9f77b13ebaaa41f55c9aad848a.png)
您最近一年使用:0次
名校
5 . 已知函数
.
(1)当
时,求
在
上的最值;(提示:
)
(2)讨论
的单调性;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fe9a4b8a4e2c28c79947d2172b5a7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b448fe164c2c2931805e3b3847dcdd75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59004c5916a745f186e0bd66aa3bca2.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a0e3f90108eb27ed9b74e51772f5df.png)
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2024-03-29更新
|
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3卷引用:山东省大联考2023-2024学年高二下学期3月质量检测联合调考数学试题
名校
6 . 已知函数
.
(1)若
,讨论
的零点个数;
(2)若
是函数
(
为
的导函数)的两个不同的零点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a441ed40dca1a0f8c5ed0253d1ca300.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab42358409a44ea7a55fe532fe66ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b550cb121a3346f8d46b7f7ee2117d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380beb181ed0a48cc486131bba4a4c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d106beb9c7a567f35e7f3407f41c963c.png)
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2024-03-27更新
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3卷引用:山东省淄博市高青县第一中学2023-2024学年高二下学期期中学分认定考试数学试题
名校
7 . 已知函数
.
(1)当
时,求函数
的最小值;
(2)当
时,
,证明不等式
;
(3)当
时,求函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d23a8dc51d70c9484d16a268d242736.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93120189134d4c08d6a991fd904596cf.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2024-03-27更新
|
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3卷引用:山东省青岛第十九中学2023-2024学年高二下学期期中考试数学试卷
名校
8 . 已知函数
是
的导函数,
.
(1)求
的单调区间;
(2)若
有唯一零点.
①求实数
的取值范围;
②当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483aa062b70c839cd5f693f23c6b94b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55506fc48681be9458f6b9cf443166ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8230f1d8b297d825b95846bc2eb1b971.png)
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2024-03-26更新
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2卷引用:山东省实验中学2024届高三下学期2月调研考试数学试卷
9 . 已知函数.
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9e6a220e85fa5a1d7c773bb143d46f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb7ac07a550b6213d94552cfe368312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb840e447985240c594ee21dcdc9db2f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bd7f157a0be7fda5ce1dca3207a957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc90bb1689796748f20d0c2a61a9c2c.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,若在
的图象上有一点列
,若直线
的斜率为
,
(ⅰ)求证:
;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9e6940a234deb9afdcbc45a450800a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7038739c261870bd71d9df8db016025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f810cd01b6c3aeb01b488f31506bd61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425f3ce645095842006c80a509268f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a3dcb9f3022b912345c5460653f5e0.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f1a4d0fb65e5a7521d49839106e4d6.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210f476a7490aea439b89218b121df8d.png)
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2024-03-21更新
|
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4卷引用:山东省济宁市第一中学2024届高三下学期3月定时检测数学试题
山东省济宁市第一中学2024届高三下学期3月定时检测数学试题山东省济宁市第一中学2024届高三下学期4月质量检测数学试卷2024届天津市十二区县重点学校一模模拟考试数学试卷(已下线)专题1 数列不等式 与导数结合 练(经典好题母题)