名校
1 . 设
,函数
,
(1)讨论
的单调性;
(2)若
有两个相异零点
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d827f87e10a7848797480161dcf3cc.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e3090a098e891e1883168719f7ad05.png)
您最近一年使用:0次
名校
2 . 如果函数
在其定义域内存在实数
,使得
成立,则称函数
为“可拆分函数”.
(1)试判断函数
是否为“可拆分函数”?并说明理由;
(2)证明:函数
为“可拆分函数”;
(3)设函数
为“可拆分函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c3f77c4d399c6ce669406032c7b7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ede389b43c78417912542746d91d00.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4a93f87af7c854415faae61d6a3770.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c16e07631b59c477c2e56ddb75f10985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-02-16更新
|
1061次组卷
|
3卷引用:云南省玉溪市玉溪一中2017-2018学年高一下学期期中考试数学试题
3 . 已知函数
.
(1)若
恒成立,试确定实数
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c80673df9fc4ceaccec5344c9e2f3a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9da98e415cc14fc6e03561a7a72d95b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3616f65644309838e78029db8d37ad9a.png)
您最近一年使用:0次
解题方法
4 . 已知椭圆
的右焦点为
,且点
在椭圆上.
(1)求椭圆
的标准方程;
(2)过椭圆
上异于其顶点的任意一点
作圆
的两条切线,切点分别为
(
不在坐标轴上),若直线
在
轴,
轴上的截距分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dfb290b1a84f670549554a0c988593.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597b9723e2ab9eab0ca81152fad8d0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda7bde4ecc7413edffcff08e2d62a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81717125fadcf1b65daddd2f216731c8.png)
您最近一年使用:0次
5 . 已知向量
,
.
(Ⅰ)求证
;
(Ⅱ)若存在不等于0的实数k和t, 使
,
满足
试求此时
的最小值.
![](https://img.xkw.com/dksih/QBM/2015/3/11/1571996161892352/1571996167847936/STEM/0e9fc92dffb1452b87b0b9d53fc6dc8c.png)
![](https://img.xkw.com/dksih/QBM/2015/3/11/1571996161892352/1571996167847936/STEM/c76ec8da26c74c07a96365acb69eb745.png)
(Ⅰ)求证
![](https://img.xkw.com/dksih/QBM/2015/3/11/1571996161892352/1571996167847936/STEM/f4c495bc8961436da3e7d498c56c50d1.png)
(Ⅱ)若存在不等于0的实数k和t, 使
![](https://img.xkw.com/dksih/QBM/2015/3/11/1571996161892352/1571996167847936/STEM/a242afa71af4439fbcc30d8997512f2b.png)
![](https://img.xkw.com/dksih/QBM/2015/3/11/1571996161892352/1571996167847936/STEM/e2211ac451bd4ce0a55bb43fe8743453.png)
![](https://img.xkw.com/dksih/QBM/2015/3/11/1571996161892352/1571996167847936/STEM/6ca182d147c94eacb0cfea6c6a95ed72.png)
![](https://img.xkw.com/dksih/QBM/2015/3/11/1571996161892352/1571996167847936/STEM/85869c9b1d9b452f957a679752891da2.png)
您最近一年使用:0次