1 . 高斯是德国著名数学家,近代数学的奠基者之一,享有“数学王子”的称号,用他名字定义的函数
称为高斯函数,其中
表示不超过x的最大整数,如
,
,已知数列
满足
,
,
,若
,
为数列
的前n项和,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1550a97c21c1d71c9e95dde569668be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54a0e82778f606d95a486835ac9f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f2323cbdf0b1b71092c962ae705102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d845281cd834068104af1b1aa6027c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7231e303ae39572f6c359c5e83822075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5735a391a46cfdbd63e171769f8abb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c3ac959bdf1b78cb98d92b87c91c46.png)
A.2026 | B.2025 | C.2024 | D.2023 |
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2023-11-25更新
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7卷引用:内蒙古赤峰市赤峰二中2024届高三上学期第三次月考数学(理)试题
内蒙古赤峰市赤峰二中2024届高三上学期第三次月考数学(理)试题云南省曲靖市第一中学2022-2023学年高一下学期7月期末考试数学试题江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题(已下线)第五章 数列 专题8 数列中的递推(已下线)第五章 数列 专题7 有关数列求通项、周期性求和的问题陕西省西安市西安中学2024届高三上学期期末数学(理)试题(已下线)4.3.2 等比数列的前n项和公式——课后作业(巩固版)
2 . 已知函数
在
处取得极值.
(1)求实数a的值;
(2)若关于x的方程
在区间
上恰有两个不同的实数根,求实数t的取值范围;
(3)证明:对任意的正整数n,不等式
都成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ccd0083aafaa8d0dd3c48edd41b4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(1)求实数a的值;
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c25b2669c1130c028447eeabc39b55d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
(3)证明:对任意的正整数n,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6c7ec8f6c6127448a724e16b096ea5.png)
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3 . 已知函数
.
(1)当
时,讨论
的单调性;
(2)令
,若
有两个不相等的实数根
.
(i)求a的取值范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c59ee61e811f2cbb69edcd7445e8d5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5466c28592d45ca35059382b351d583f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(i)求a的取值范围;
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0fd6297d9af0dbfaccd08a53054ec5.png)
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4 . 已知函数
.
(1)讨论函数的单调性;
(2)若
有两个不同的零点
,不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254c07941a6929e0afa818a7a2176657.png)
(1)讨论函数的单调性;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2217a4ab9fc9692c87c43ed4f02a240a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec97fb7fc62f40059a13e7e69ac40e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8be675c8d80f2d734b32f929ec1493.png)
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2023-05-12更新
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483次组卷
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2卷引用:内蒙古赤峰二中2022-2023学年高二下学期第二次月考数学(理)试题
解题方法
5 . 已知椭圆
的离心率为
,其左、右顶点分别为
,
,左、右焦点为
,
,点
为椭圆上异于
,
的动点,且
的面积最大值为
.
(1)求椭圆
的方程;
(2)设过定点
的直线交椭圆
于
,
两点(与
,
不重合)证明:直线
与直线
的交点的横坐标为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e4a3aea4b4b0d87c014030a6ff9027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
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6 . 已知函数
,其中
.
(1)若
有两个零点,求
的取值范围;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca21eedd5ab308bec2757f28920aab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b6f26d5322f743d01274b1b921829da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-04-19更新
|
3053次组卷
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11卷引用:内蒙古锡林郭勒盟2024届高三上学期第二次统一考试(12月月考)(全国乙卷)文科数学试题
内蒙古锡林郭勒盟2024届高三上学期第二次统一考试(12月月考)(全国乙卷)文科数学试题广东省佛山市2023届高三二模数学试题(已下线)押新高考第22题 导数综合解答题(已下线)专题09 函数与导数-2专题07导数及其应用(解答题)湖南省岳阳县第一中学2023届高三二模数学试题2024届高三第一次统一考试(全国乙卷)理科数学试题湖北省黄冈市黄梅国际育才高级中学2023-2024学年高三上学期11月期中数学试题(已下线)第九章 导数与三角函数的联袂 专题三 含三角函数的恒成立问题 微点3 三角函数的恒成立问题(三)宁夏回族自治区银川一中2024届高三下学期第一次模拟考试数学(理)试题湖北省武汉市华中科技大学附属中学2024届高三高考适应性考试1数学试题
名校
解题方法
7 . 已知函数
有两个不同的极值点
,且不等式
恒成立,则实数t的范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f821ff0a8561d8ca7dd8fbf40ddaa67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c785f0c80cd698b3e97a9f020d4ac0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-04更新
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4卷引用:内蒙古呼伦贝尔市满洲里市第一中学2022-2023学年高二下学期期中考试数学理科试题
8 . 已知
和
分别是函数
(
且
)的极小值点和极大值点.若
,则
的最小值的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971905ea129aec0ca7c325f60260c7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd86badb20015aa65328fda1e43a117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c46411497efa3caaa76c541d7a34a0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d276b856da9c46e1b0912fbdac6962a.png)
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9 . 已知函数
.
(1)若
,试判断
的单调性,并证明你的结论;
(2)若
恒成立.
①求
的取值范围:
②设
,
表示不超过
的最大整数.求
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7097cfdb660880508c976c4ac9fdbf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d58b0c51f8c4d876af791576ed6ffcd.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea98bde5af87727ddf5e63715708986f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a0b88c37278b5dddd555b3442f0519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405361d7be3c9e4d462a4e955d8fe3c.png)
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2023-03-03更新
|
1420次组卷
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2卷引用:内蒙古赤峰二中2022-2023学年高二下学期第一次月考数学(理)试题
10 . 已知函数
.
(1)若
存在极值,求
的取值范围;
(2)当
时,讨论函数
的零点情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a970882dcc8b8f54905841c10e6e3a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556eac935a69ae56fb1d63bee5a1e5dc.png)
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