解题方法
1 . 已知函数
有两个零点
.
(1)求实数a的取值范围;
(2)求证:
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40fa8f8f5b08ba22c03f57d82b5445f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(1)求实数a的取值范围;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfcbdd81ba24d15dcb3af31f8942b0ab.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7b02489f088df9ba0c7eefbd1c6055.png)
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2 . 已知函数
.
(1)讨论
的单调性;
(2)设
,对于任意
,均存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ff6000c8f8083e89a9f47c018fdae7.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738a40a8284c6eb093b0382c06e04d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1760522e30613a463766f77d936429e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a074019a75a26e8d6b9147731a29a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6154e00013d9dee84c0e941f676ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
3 . 设,函数
的图象与直线
相切,其中
是自然对数的底数.
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5791e3050af8940d9376dcef24fbcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5c575383648f85b2d47e9d550f28b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 已知直线
方程为
,点
,点
到点
的距离与到直线
的距离之比为
,
.
(1)求点
的轨迹
的方程(用
表示);
(2)若斜率为
的动直线
与(1)中轨迹
交于点
,
,其中
,
.点
(
)在轨迹
上,且直线
、
与
轴分别交于
、
两点,若恒有
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e756c89b600e37dfb36bb22ef28eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4cc00c283519973f7f8e1274b5c733.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891fe97a26ca688e22e5d704432f764b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b170470d02c85c1be9a3faff5eca0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374e2198b495b86b0f8308d28035a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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5 . 定义:设二元函数
在点
的附近有定义,当
固定在
而
在
处有改变量
时,相应的二元函数
有改变量
,如果
存在,那么称此极限为二元函数
在点
处对
的偏导数,记作
.若
在区域D内每一个点
对
的偏导数都存在,那么这个偏导数就是一个关于x,y的二元函数,它就被称为二元函数
对自变量
的偏导函数,记作
.已知
,若
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e664fa90a859ab05fe49972a474a5fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1268e217016ff7e12b9bc51341c4cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e664fa90a859ab05fe49972a474a5fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81443d23814e97aca7dc31d6a6761e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b46f5293a40631887c03efab57a24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e664fa90a859ab05fe49972a474a5fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205aa63ae7eac640729254cccc919a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e664fa90a859ab05fe49972a474a5fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e664fa90a859ab05fe49972a474a5fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d827cd88fa489081f6de96c9b1949d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a0767e51cf2027ba71e6ec233b3de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4642bed61cb89af0efa1c53294541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bc92eb72cfdadd35f9f514090b40b8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:高二 模块3 专题1 第4套 小题进阶提升练(苏教版)
(已下线)高二 模块3 专题1 第4套 小题进阶提升练(苏教版)(已下线)高二 模块3 专题1 第4套 小题进阶提升练江西省2024届高三上学期12月统一调研测试数学试题江西省赣州市大余县部分学校2024届高三上学期12月统一调研测试数学试题
6 . 如图所示,四边形ABDC为梯形,其中
,O为对角线的交点.有4条线段(GH、KL、EF、MN)夹在两底之间.GH表示平行于两底且于他们等距离的线段(即梯形的中位线),KL表示平行于两底且使梯形ABLK与梯形KLDC相似的线段,EF表示平行与两底且过点O的线段,MN表示平行于两底且将梯形ABDC分为面积相等的两个梯形的线段.下列说法中正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/616ad507-dd52-430e-8e57-aceee5e77449.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92b09f88aee4ed088bf9b86fd5bc53b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/616ad507-dd52-430e-8e57-aceee5e77449.png?resizew=171)
A.若![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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7 . 已知函数
.
(1)讨论函数
在
上的单调性;
(2)当
时,
①判断函数
的零点个数,并证明.
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea8ddadb910710765fb78ca1696c10b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c6b9fa72109ba69163a5c6b7874a2.png)
①判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1350cb142ba647b1a96ed5d7063665.png)
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8 . 已知函数
,下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1c764d362bd30119c4b850f3265a31.png)
A.函数![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若过点![]() ![]() ![]() ![]() |
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江苏省启东市2023-2024学年高三上学期期中质量监测数学试卷山东省泰安市新泰弘文中学2024届高三上学期第二次质量检测数学试题广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(一)(已下线)第五章 一元函数的导数及其应用(压轴题专练,精选34题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)(已下线)专题10 切线问题(过关集训)(已下线)模型8 放大镜与函数整数问题模型
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9 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a7d37824a7e361d0cfcfdb372c87e7.png)
A.函数![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.不等式![]() ![]() ![]() ![]() |
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解题方法
10 . 已知函数
,
是定义在
上的函数,其中
是奇函数,
是偶函数,且
,若对于任意
,都有
,则实数
可能的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](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/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0dec2f7aa4eb98c9804ecc89057f73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adb2f27ddb3d3acf4eda4f1a5e47e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e66a2a8a5fe171f42e1ab414f7d3cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.0 | C.![]() | D.1 |
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