1 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f4f5e77f6d454d5b08b94bcaa6fdce.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() ![]() |
您最近一年使用:0次
解题方法
2 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d72c2d25e0a42a67d97122a906863bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e6096f2e89af886f2f744367588a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0f8a97ff297c96f4118993483648d6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 已知函数
,
是函数
的导函数,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8399f466be639dfa3e612466888b64a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
A.![]() |
B.![]() |
C.若函数![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
名校
4 . 已知函数
是定义在
上的奇函数,且当
时,
.
(1)求
时,函数
的解析式;
(2)若函数
的最小值为2,求实数
的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ed92f58d44ee590c425bc741195c1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e9e7cd22283f191a70656dd0af826d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
5 . 狄利克雷是德国著名数学家,函数
被称为狄利克雷函数,下面给出关于狄利克雷函数
的结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d1a0e2dca4d9b89193c869e6c989a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8238fba9b391d01ceb071e78ee221035.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知
的定义域为
,且
恒成立.
(1)求
的值;
(2)试判断
的单调性,并用定义证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae3a16b9fab158f4d46ff236860d39e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cb3110d75667298a8173aee405a017.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
7 . 关于
的方程
有四个不相等的实数根,则实数
的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0710bedaa1ec8021a98503c16526dfdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
8 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f982b548222f754ce396d53bbc02aa5.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
9 . 已知函数
的部分图象如图所示,则
的解析式可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
10 . 函数的凹凸性的定义是由丹麦著名的数学家兼工程师Johan Jensen在1905年提出来的.其中对于凸函数的定义如下:设连续函数
的定义域为
(或开区间
或
,或
都可以),若对于区间
上任意两个数
,均有
成立,则称
为区间
上的凸函数.容易证明譬如
都是凸函数.Johan Jensen在1906年将上述不等式推广到了
个变量的情形,即著名的Jensen不等式:若函数
为其定义域上的凸函数,则对其定义域内任意
个数
,均有
成立,当且仅当
时等号成立.
(1)若函数
为
上的凸函数,求
的取值范围:
(2)在
中,求
的最小值;
(3)若连续函数
的定义域和值域都是
,且对于任意
均满足下述两个不等式:
,证明:函数
为
上的凸函数.(注:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b3dce3b2dd078fdd6b4cfd301927f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0c0214295e38221c4e98d13a8b6b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1bedaf3854b48806b82b3b804451cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2d0d76b383beb0f422ed02a2b888b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83590c4a7ea5636843dd4b60c67cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae7a1a59fbb460ff17c32dc7e3bb4ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73223617c8855826298d435673787a94.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165c6db50a97f8ed52b759e57ba2644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82822f0c261ac2193ef264fe68321833.png)
(3)若连续函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9484fcea82180e9886a18d7a947b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963c40a0a3722b8f432ee37eef7cb1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa06f4df6281bd147ce5bd8332cfb66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56b9605ab2765c9811e9432e38d905e.png)
您最近一年使用:0次