1 . 已知函数
,其中
.
(1)若
,证明:
时,
;
(2)若函数
在其定义域内单调递增,求实数
的值;
(3)已知数列
的通项公式为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc918d83961931831f58ee6ee88ce37f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3647a896689efaec8ae89cad1cd845d5.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4633de9335d15d7685bdecb007a3678c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd30509fe23160914e2cea22efe4b101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccc81f3cbaab5987151e4235b3600f8.png)
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2024-06-08更新
|
257次组卷
|
2卷引用:黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期阶段考试(二)数学试题
名校
解题方法
2 . (1)若
,
,求
的取值范围;
(2)证明:
;
(3)估计
的值(保留小数点后3位).
已知
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fad1dd76d5b72f10f5bb62693a2996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c37e166515544d73dfcf03cdc084d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3a73ba5ea3b9218649d350387a3f83.png)
(3)估计
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e24d42f61784c642e9eb1316afdd2ad.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695450724faafa68f7acabe8a3b504b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d230beb82a9f553b1e3e7cc7cd15d7f1.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)当
时,求证:
①当
时,
;
②函数
有唯一极值点;
(2)若曲线
与曲线
在某公共点处的切线重合,则称该切线为
和
的“优切线”.若曲线
与曲线
存在两条互相垂直的“优切线”,求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7f41aa561904f6f2a8e6aaae348855.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42342632cbd8e9cfbae17b76d94b033.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e5ea144897b9b7db92726da39648f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2024-01-18更新
|
1288次组卷
|
2卷引用:黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期得分训练数学试卷(一)
名校
4 . 已知函数
.
(1)求
的单调区间;
(2)若
,函数
.
(i)证明:
在区间
上存在极值点;
(ii)记
在区间
上的极值点为
在区间
上的零点的和为
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacaf2470a32d4348c0d6b821ffbb4cf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00cf17a6705ecbf93191924edb9e11e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdbb5162cb76bfce5cd7c5f75e6e874.png)
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2024-01-11更新
|
654次组卷
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3卷引用:黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期得分训练(三)数学试卷
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1992673f2428acad25b02245ce76d589.png)
(1)讨论
的单调性;
(2)证明:当
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1992673f2428acad25b02245ce76d589.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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2023-11-14更新
|
659次组卷
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3卷引用:黑龙江省大庆市林甸县第一中学2024届高三上学期12月阶段考试数学试题
名校
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
(1)若
,证明:
在
上恒成立;
(2)若方程
有两个实数根
且
,证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d889f2c38ab7df7a03aedb3e9d28ea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8eca68c4c7478f412183aa275fc7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6adb82c401086b3536212bb06125eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a20570016dcade92a03583ca7a74a8.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809a06357f94fc7a2156c7e7af1ed2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d889f2c38ab7df7a03aedb3e9d28ea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
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2023-10-29更新
|
587次组卷
|
3卷引用:黑龙江省大庆实验中学2023-2024学年高三上学期期中考试数学试题
名校
解题方法
7 . 已知函数
,
,且曲线
和
在原点处有相同的切线.
(1)求实数a的值:
(2)证明:当
时,
;
(3)令
,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82677d95bc109795e16401461dc6467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591d032abe536b6bfc4e04104dc921bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)求实数a的值:
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e96e2ed7d9cd25c06f9a51a7210a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d3ac6f2ecceac9566cdc98752ba2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343143dd8a6ce47f1ea1a32478a8a49e.png)
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2023-10-24更新
|
383次组卷
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2卷引用:黑龙江省大庆市大庆实验中学2021年高三上学期10月月考数学试题
名校
8 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70566518997abd6bf0afabe06807b785.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11cf3ca4a89057b9e7a11be36ac7bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b8da5de0594db80f92dfcbe857b537.png)
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2023-08-27更新
|
1047次组卷
|
5卷引用:黑龙江省大庆市2024届高三第一次教学质量检测数学试题
黑龙江省大庆市2024届高三第一次教学质量检测数学试题广东省部分学校2024届高三上学期8月第二次联考数学试题河南省洛阳市洛宁县第一高级中学2023-2024学年高三上学期第一次月考数学试题陕西省2024届高三上学期第一次联考理科数学试题(已下线)考点20 导数的应用--不等式问题 2024届高考数学考点总动员【练】
解题方法
9 . 已知函数
.
(1)若
,证明:当
时,
恒成立;
(2)若
是函数
的极大值点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bd2a394e4ada010d45c22788d524c9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5efe66db991b562c73ffb16c1e585870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,
,求实数a的取值范围;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43cd787e8daf9196d47a0247c75529f.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce009f8708c898ce73d1b6d38323f46.png)
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