解题方法
1 . 已知函数
在区间[1,2]上单调递增,则实数a的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7099112b4aaca7cc9454781b0532c2f.png)
A.1 | B.![]() | C.![]() | D.![]() |
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2 . 袋子中有若干除颜色外完全相同的黑球和白球,在第一次摸到白球的条件下,第二次摸到黑球的概率为
,第一次摸到白球且第二次摸到黑球的概率为
,则第一次摸到白球的概率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2008b78a906cf5ecdfd68432fa9ad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1985174e05ad371e13cf24d244423da4.png)
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3 . 已知等差数列
的公差d≠0,且
,
,
成等比数列,
的前n项和为
,
,设
,数列
的前n项和为
,
(1)求数列
的通项公式;
(2)若不等式
对一切
恒成立,求实数λ的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d04a8b7a7595251251b8e0b7e665e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc3df3bea2def2fd30b0f90d75ef32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666c4baf8ded0a8c4788b67f316e81f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f39fbe22dd891ead500de7e77ab3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0a11035037cfd4240c48bc89661374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e922c4273aaef507f569cf67ab3d6537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
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解题方法
4 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57275a39e0ff5a72b93fa22dd9e3357.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
5 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
恒成立,求
的取值范围;
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536d662ffb82903b39d82d7053aadd2f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302337058242c7b78e3eb4ac7210b7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40d5295942e85ec07a3728c7ad308d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b0c3cf87f438d1fe0f6fca51b40be2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e75f547129d14ffb61324fb58492ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db9ea9575be1bdcd679099b47e45c23.png)
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6 . 已知数列
的通项公式为
,在
与
中插入
个数,使这
个数组成一个公差为
的等差数列,记数列
的前
项和为
,
(1)求
的通项公式及
;
(2)设
,
为数列
的前
项和,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a2150c288b258addb66ae22ae818de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9acc937f669c8c7378303432f76aa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6469fad168bbcdf117f29fdbe26c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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4卷引用:四川省泸州市龙马潭区2023-2024学年高二下学期6月期末考试数学试题
四川省泸州市龙马潭区2023-2024学年高二下学期6月期末考试数学试题江西省南昌市第十九中学2023-2024学年高二下学期5月期中考试数学试题湖北省武汉市第十一中学2023-2024学年高二下学期6月考数学试题(已下线)专题07 数列通项公式与数列求和--高二期末考点大串讲(人教B版2019选择性必修第三册)
名校
解题方法
7 . 关于
的不等式
有解,则实数
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b021b127a6d00ae353a46bf995427923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 已知
,
,对任意的
都有
,则
的取值范围是_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c78fc54dee0dee8c889114611906df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83655a9220769796fe153f023528c91f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae828be829213bd6b66651dce99263c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
9 . 用数学的眼光看世界就能发现很多数学之“美”.现代建筑讲究线条感,曲线之美让人称奇,衡量曲线弯曲程度的重要指标是曲率,曲线的曲率定义如下:若
是
的导函数,
是
的导函数,则曲线
在点
处的曲率
.
在
处的曲率
的平方;
(2)求余弦曲线
曲率
的最大值;
(3)余弦曲线
,若
,判断
在区间
上零点的个数,并写出证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bac50c92211d6348b056335f6c83ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e669b77945df783df093b549ac2a67d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bdb811e83e6f94b20dfa3ab68b1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391039b1ebf01aa7def8a44c97ea05b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9311b13eb2baab6641da9e7b48e13e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e029cc1f7d07eeb136bd3946a7eb23e3.png)
(2)求余弦曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d87f3c6bd439ef3d84a6c6da3642e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32410867843f1a7ef11410da8f3f8dab.png)
(3)余弦曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d87f3c6bd439ef3d84a6c6da3642e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbffb683ddd3767c5ebd35ac9212f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877e6c30566e9d9b11ecf5b78f4c5e73.png)
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10 . 已知关于
的不等式
(其中
)的解集中恰有两个整数,则实数
的取值范围是_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a9ee364e657e34bea8b4e808bd8c1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe90bc702b45f98d6c2eed989ffccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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