名校
解题方法
1 . 设定义在
上的函数
的导函数为
,若满足
,且
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db17c0ebab844dad112b5b2c50551a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91770acb583f05c3ead767d247be034.png)
A.![]() ![]() |
B.不等式![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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解题方法
2 . 已知函数
有两个零点.
(1)求
的取值范围;
(2)函数
,若
与
有相同的值域,求
的值,并证明:
,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eeff8c7b49ab069f5e30fae6e168c68.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f697374185dd40c8fc4e7d2a62d15e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d794c3af7140c07ef04547cdd0be19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b002c375a4530b092286b818d449ee.png)
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名校
解题方法
3 . 已知函数
.
(1)当
,
时,求证
恒成立;
(2)当
时,
,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47850d9a29a648cac2648a72e1e0000.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0d0d6f49220326be0bc66e8d1f814f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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|
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4 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87502edfb6d853164e6c98eebfcef09f.png)
A.函数![]() ![]() |
B.函数![]() ![]() |
C.若方程![]() ![]() ![]() ![]() |
D.当方程![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
5 . 在函数极限的运算过程中,洛必达法则是解决未定式
型或
型极限的一种重要方法,其含义为:若函数
和
满足下列条件:
①
且
(或
,
);
②在点
的附近区域内两者都可导,且
;
③
(
可为实数,也可为
),则
.
(1)用洛必达法则求
;
(2)函数
(
,
),判断并说明
的零点个数;
(3)已知
,
,
,求
的解析式.
参考公式:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955689923ebe1be46168295644f4a178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef9c42b3bfeac3b11f6f2f7c5227967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7490f915131bdb436285e3fb284817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba30ad5f21a62879bba0aee45b81507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e530f639eaa27858ed7db451e2ed576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4658c5369aa8a25ea8580f524e87da.png)
②在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90c83ba8da83994264cb5b8b2f15f4.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56af5e590e8152c9a7ded6209e446ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de3f06b6df7b949c5e6b406a661079f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f32baa7d29934cde8a5203388ed18c6.png)
(1)用洛必达法则求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782ec35f212cb1448863b4b15e806814.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161ab6e6a97905ea5bb2b3fc390ab7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deda945164283569437cda6976fe35ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddd2a1b30b9ad891172f7f21c5a2701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc2b7be871fef904c94ef6360ee32bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f385eacc118fe9b5f0c23182929d6a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9005b464218c70a9963452693645cf2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9949db821a880972efbfb32354cd6bd.png)
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2024-04-24更新
|
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|
4卷引用:河南省郑州市宇华实验学校2024届高三下学期5月月考数学试题
名校
解题方法
6 . 已知函数
和其导函数
的定义域都是
,若
与
均为偶函数,则( )
![](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/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c822c874e9ccc9ed9e0d126b01ce9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143d920763bb59b1a8f86d9865580025.png)
A.![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
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13卷引用:河南省信阳市新县高级中学2024届高三下学期3月适应性考试数学试题
河南省信阳市新县高级中学2024届高三下学期3月适应性考试数学试题浙江省金华十校2024届高三上学期11月模拟考试数学试题(已下线)专题02 函数及其应用、指对幂函数(5大易错点分析+解题模板+举一反三+易错题通关)江西省赣州市南康中学2024届高三“九省联考”考后模拟训练数学试题(一)安徽省合肥一六八中学2024届高三“九省联考”考后适应性测试数学试题(一)湖南省2024年高三数学新改革提高训练三(九省联考题型)2024届广东省新改革高三模拟高考预测卷一(九省联考题型)数学试卷(已下线)黄金卷05(2024新题型)(已下线)黄金卷02(2024新题型)(已下线)专题02 函数与导数(已下线)第2题 复合函数与抽象函数(压轴小题6月)湖南省衡阳市第八中学2024届高三适应性考试数学试题辽宁省沈阳第二中学2024届高三第四次模拟考试数学试卷
7 . 已知函数
有两个零点
,
.
(1)求实数
的取值范围;
(2)如果
,求此时
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3420aafbf36a4570fe8de7da2d18f74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4054a751322402b8be781807be4e66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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|
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河南省信阳市新县高级中学2024届高三4月适应性考试数学试题湖北省黄石市第二中学2023-2024学年高三下学期三模考试数学试题(已下线)专题02 利用导数求解函数极值及最值问题(四大类型)(已下线)宁夏回族自治区银川一中2024届高三下学期第四次模拟数学(文)试卷宁夏回族自治区银川一中2024届高三下学期第四次模拟考试数学(文)试卷
名校
解题方法
8 . 设函数
,
.
(1)若
,求函数
的单调区间;
(2)若
,试判断函数
在区间
内的极值点的个数,并说明理由;
(3)求证:对任意的正数
,都存在实数
,满足:对任意的
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cd1c5271c733796702224a1fb20afd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d0bd8cf72d1f49cf9e6510f43410b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c99179b6beb5b95219b50cf0718f6a9.png)
(3)求证:对任意的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0235c71a9122457ffd395f4e0c8f53ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79d191df58c2dd16811fc9aa2de48b9.png)
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9 . 若实数
分别是方程
,
的根,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf7fd898b29856117f9e2b9ece8c74c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac036ac82989e301088b9c898e00e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b953e06f7a01faeace7176ddd2d77c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf7fd898b29856117f9e2b9ece8c74c.png)
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名校
10 . 设函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e93467ac54cad705e88f09d3d74ce6.png)
A.函数![]() ![]() |
B.曲线![]() ![]() ![]() |
C.函数![]() |
D.若方程![]() ![]() |
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