1 . 已知函数
.
(1)讨论函数
的单调性;
(2)若函数
与
的图象恰有一对点关于
对称,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe64c3eaf3e9a2fecc3bdc4bb996b4c.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 若函数
在定义域内有两个极值点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36ad6537251806cbe34b6d30b0250c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-22更新
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5卷引用:湖南省郴州市2023-2024学年高二上学期期末教学质量监测数学试卷
湖南省郴州市2023-2024学年高二上学期期末教学质量监测数学试卷(已下线)5.3.2课时1函数的极值 第三练 能力提升拔高重庆市礼嘉中学2023-2024学年高二下学期第一次月考数学试题海南省琼海市嘉积中学2023-2024学年高二下学期高中教学第二次大课堂练习数学试题(已下线)专题01 一元函数的导数及其应用-3
3 . 大衍数列来源于《乾坤谱》中对易传“大衍之数五十”的推论,主要用于解释中国传统文化中的太极衍生原理,数列中的每一项都代表太极衍生过程中,曾经经历过的两仪数量总和,它是世界数学史上第一道数列题.已知大衍数列
满足
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1d022fbfa1d61291bf532198b3e713.png)
A.![]() |
B.![]() |
C.此数列的前![]() ![]() |
D.数列![]() |
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4 . 已知椭圆
的离心率为
,双曲线
的离心率为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e376b48dacaa422f4d21afe48c32523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-12-29更新
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10卷引用:湖南省郴州市嘉禾县第一中学2021-2022学年高二上学期期末模拟数学试题
湖南省郴州市嘉禾县第一中学2021-2022学年高二上学期期末模拟数学试题青海省西宁市大通回族土族自治县2021-2022学年高二上学期期末考试数学(理)试题青海省西宁市大通回族土族自治县2021-2022学年高二上学期期末考试数学(文)试题青海省海南藏族自治州高级中学2021-2022学年高二上学期期末考试数学(理)试题青海省海南藏族自治州高级中学2021-2022学年高二上学期期末考试数学(文)试题陕西省咸阳市永寿县中学2022-2023学年高二上学期第三次月考文科数学试题吉林省四平市第一高级中学2021-2022学年高二上学期第三次月考数学试题山西省介休市第一中学校2022-2023学年高二上学期12月月考数学试题河南省焦作市第一中学2022-2023学年高二下学期4月模拟检测数学试题四川省成都市高新实验中学2023-2024学年高二上学期12月月考数学试题
5 . 如图,正方形
中,边长为4,
为
中点,
是边
上的动点.将
沿
翻折到
沿
翻折到
,
平面
;
(2)若
,连接
,设直线
与平面
所成角为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afeff57a058eb3baf1eea60088fff06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094cdaea0090d45556d38bf1420cf04a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365a785ab5fa2dc8d2fdb07545e3772c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4457b0fbba18bae1cf18cb5947a144c1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17baac332fe2f27b0ba4f1cfeab1ae45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c157ff302a881c17514534903c575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2023-07-14更新
|
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3卷引用:湖南省郴州市2022-2023学年高二下学期期末数学试题
解题方法
6 . 已知双曲线
的一条渐近线方程为
,且左焦点
到渐近线的距离为
,直线
经过
且互相垂直(斜率都存在且不为0),与双曲线
分别交于点
和
分别为
的中点.
(1)求双曲线
的方程;
(2)证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc261508f42e75323971f0b8282b0ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6426a6960d726b7378b7ceeb2f77b148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71dcfcf229802e12eb90ef71a837cba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba0eb957c274d93b74cb4d4d88f7f39.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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7 . 已知函数
,
,
,其中
为自然对数的底数.
(1)讨论
的单调性;
(2)当
时,证明:对于
,都有
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f4ce63ecec208598b23202ae211bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a638b5a60d9a3dc23e23b5472874f785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fad1dd76d5b72f10f5bb62693a2996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
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2023-04-21更新
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476次组卷
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3卷引用:湖南省郴州市嘉禾县第六中学2022-2023学年高二下学期第二次月考数学试题
名校
解题方法
8 . 已知函数
,
.
(1)若
在
上恒成立,求k的取值范围;
(2)设
为
图象上一点,
为
图象上一点,O为坐标原点,若∠AOB为锐角,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf266c400ec9f20afcdb1c76a62c6c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27bcb0a5f3d22e9df052879fb0d0d4d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc1df6dfa5bb84b0f213a00a11d1a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb2a536197b222df8b10a4c453f05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eae6fbe53a949c340ddcc6d3067f068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ca0e0b071265e90852d22ef88de865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773c2bb351fa6cfcf69ad75b63395cbe.png)
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2023-04-15更新
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253次组卷
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2卷引用:湖南省郴州市2022-2023学年高二下学期期中数学试题
名校
解题方法
9 . 已知函数
存在两个极值点
,
,且
,则a的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57c9d084045321285f1a82f69b02f50.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/3058bb0695d0f878b2689afcf6d8592c.png)
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2023-04-15更新
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397次组卷
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2卷引用:湖南省郴州市2022-2023学年高二下学期期中数学试题
名校
解题方法
10 . 已知F为抛物线
的焦点,O为坐标原点,过点
的直线与抛物线交于A,B两点,且满足
.
(1)求
的值;
(2)若
,求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3334308760163eebfb7fcf1c92cfe604.png)
您最近一年使用:0次
2023-04-15更新
|
187次组卷
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2卷引用:湖南省郴州市2022-2023学年高二下学期期中数学试题