名校
1 . 已知函数
.
(1)当
时,讨论函数
的单调性;
(2)若不等式
恒成立,求
的取值范围;
(3)在(1)的条件下,设
,
,且
.求证:当
,且
时,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e7bafcc08b76256e0ec491fb36f712.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6ea20aa7804cb6e41322bc3d8dc99b.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810e8fa5cf17ae94a41803772c488726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)在(1)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf2a234b8102356b2c13a3c0b75a00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c0c165afc6ed30f0d41808f8442f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5922c1719da2520a49b75db30ab0c276.png)
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解题方法
2 . 现有编号为1,2,3的三个口袋,其中1号口袋内装有两个1号球,一个2号球和一个3号球;2号口袋内装有两个1号球,一个3号球;3号口袋内装有三个1号球,两个2号球;第一次先从1号口袋内随机抽取1个球,将取出的球放入与球同编号的口袋中,第二次从该口袋中任取一个球,下列说法不正确的是( )
A.在第一次抽到3号球的条件下,第二次抽到1号球的概率是![]() |
B.第二次取到1号球的概率![]() |
C.如果第二次取到1号球,则它来自1号口袋的概率最大 |
D.如果将5个不同小球放入这3个口袋内,每个口袋至少放1个,则不同的分配方法有150种 |
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3 . 设
,函数
. 若
在区间
内恰有2个零点,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b855d201ea3903374586b03606a016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 设
是等差数列,其前
项和
,
是等比数列,且
,
,
.
(1)求
与
的通项公式;
(2)设
,求数列
的前
项和
;
(3)若对于任意的
不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85444874c705666de9488286d3d61dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1273751a0b5a984cf01c2d0e00e474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9651204c54475c2e8cda8d0a6eeba177.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca3f045d6f1fbdf6feedaf05363575b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2771c5f04582c545e0f9afc8a2cb9597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161ac25d7a41e3e2b5bbb4166153ad4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
5 .
的内角
的对边分别为
已知
.
(1)若
的周长等于3,求
;
(2)若
为锐角三角形,且
;
①求
;
②求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c5353aa379b38ff11ce0e79200bd14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbedf6a68d2dd2ef0ca9faa7903d39a.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
6 . 已知袋子中有a个红球和b个蓝球,现从袋子中随机摸球,则下列说法中正确的是_________ .
①每次摸1个球,摸出的球观察颜色后不放回,则第2次摸到红球的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd09f80733a8c98bd8c51905d15fe5.png)
②每次摸1个球,摸出球观察颜色后不放回,则第1次摸到红球的条件下,第2次摸到红球的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127098d6950b3458c216fca72e40b58e.png)
③每次摸出1个球,摸出的球观察颜色后放回,连续摸n次后,摸到红球的次数X的方差为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278ac048121c43a530c9e418b2830eb9.png)
④从中不放回摸
个球,摸到红球的个数X的概率是
①每次摸1个球,摸出的球观察颜色后不放回,则第2次摸到红球的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd09f80733a8c98bd8c51905d15fe5.png)
②每次摸1个球,摸出球观察颜色后不放回,则第1次摸到红球的条件下,第2次摸到红球的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127098d6950b3458c216fca72e40b58e.png)
③每次摸出1个球,摸出的球观察颜色后放回,连续摸n次后,摸到红球的次数X的方差为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278ac048121c43a530c9e418b2830eb9.png)
④从中不放回摸
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0c8b22fe5f66c0a953253dbb5bc987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7be80ee5cb699eea5f3359d754de26.png)
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2024-05-09更新
|
407次组卷
|
2卷引用:天津市静海区第一中学2023-2024学年高二下学期6月学业能力调研数学试题
名校
解题方法
7 . 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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2024-04-13更新
|
1082次组卷
|
7卷引用:天津市武清区杨村第一中学2024届高考数学热身训练卷
天津市武清区杨村第一中学2024届高考数学热身训练卷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】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
解题方法
8 . 点O是平面
上一定点,A,B,C是平面
上
的三个顶点,
,
分别是边AC,AB的对角.有以下四个命题:
①动点P满足
,则
的外心一定在满足条件的P点集合中;
②动点P满足
,则
的内心一定在满足条件的P点集合中;
③动点P满足
,则
的重心一定在满足条件的P点集合中;
④动点P满足
,则
的垂心一定在满足条件的P点集合中.其中正确命题的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
①动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194928662ef5170ec329fa0839e96810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f06ef8a11b1b7e4977bd57fbf89aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
③动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34459872490d5f5a616999415532470a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
④动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b31a28180fdba611bcaedadbddd67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
9 . 已知向量
;定义函数
,称向量
为
的特征向量,
为
的特征函数.
(1)设
,求
的特征向量;
(2)设向量
的特征函数为
,求当
且
时,
的值;
(3)设向量
的特征函数为
,记
,若
在区间
上至少有40个零点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9987768637e8aa2fe051499381acc3d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c6e203b4b2ddb496ba5e241140051d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7426e927be203401a7ea80f7e35e3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d806f27eecf5aee1e75bf35acbcd4c.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09853b4ab5476d41940f81de7985c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c5022fcadbebddb7be00d5a8d79c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a23ec821b5896710d79bfe703cec01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f5a04aef63712bb14cd11854ab79b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8c56d09485b718a85ed23f637e2d77.png)
(3)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b059c2d0041f3f0ae98e3995b723c289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354a3bc958749d6abbcfe8f29bc79773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
您最近一年使用:0次
2024-04-07更新
|
216次组卷
|
2卷引用:天津外国语大学附属河北外国语中学2023-2024学年高一下学期第一次月考数学试题
10 . 若某类数列
满足“
,且
”
,则称这个数列
为“
型数列”.
(1)若数列
满足
,求
的值并证明:数列
是“
型数列”;
(2)若数列
的各项均为正整数,且
为“
型数列”,记
,数列
为等比数列,公比
为正整数,当
不是“
型数列”时,
(i)求数列
的通项公式;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b781279c765cfbfb88b28bc5b6cfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be613fff0421d9be9e8bb5eb8b07c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cf22c8daa450289ffdce46b85024b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85726f99979d3793ea28b77a7708f4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(i)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15b6cf3d2cdd85baed3056ac375d3c.png)
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