真题
解题方法
1 . A是由定义在
上且满足如下条件的函数
组成的集合:①对任意的
,都有
;②存在常数
,使得对任意的
,都有
.
(1)设
,证明:
;
(2)设
,如果存在
,使得
,那么这样的
是唯一的;
(3)设
,任取
,令
,证明:给定正整数k,对任意的正整数p,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de71d25c72850e383a4c841eed0db99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2775ffdf695af2d263f0ea93ac5904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4031c9cbbcbbecfc0a8ca5490647e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5d880d349c00a3f81f830bb35e1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d03b29af4e3206af656a142d17657f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799650ddf5fb8e7c91cf59163aa1b7a4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1dbdb8423d86a92629b081ae2b2154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5528f643fe7e0449e48c8f81b16b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e599070e5874ed4a9478f5260b98e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0d7024ce3371628f09963f9a976ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dcca902b1982e13aeea5d094bb6016.png)
您最近一年使用:0次
真题
2 . 设
是定义在区间
上的函数,且满足条件:
①
;
②对任意的
,都有
.
(1)证明:对任意的
;
(2)证明:对任意的
;
(3)在区间
上是否存在满足题设条件的奇函数
;且使得
,若存在,请举一例;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ccafcfb1b2a1cd2e09b41b866654c1.png)
②对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7954415c9cb58888eb0acac8fc0f4e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b35d04b675865c0d4de71cdd5615b2b.png)
(1)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f036c33ff1b8e236cb8532f82e3018c7.png)
(2)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18786ca8c315be4161ed481cfc395406.png)
(3)在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8e293767446d82f7711d77f992d45b.png)
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真题
3 . 已知
,
,
是实数,函数
,
,当
时,
.
(1)证明:
;
(2)证明:当
时,
;
(3)设
,当
时,
的最大值为2,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd0587f5d6a3b5db9e4a93e0dbc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634952be20c76e0701e80675318830fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343069217cd6d8dd32446da428dae46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d026de72fab7e92f39f461e41be3a15.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad65bf2079957540f50eb71280ec3c46.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343069217cd6d8dd32446da428dae46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91332074f41dd2bd2588b5fcb5f829e7.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343069217cd6d8dd32446da428dae46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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真题
4 . 若
为常数,且
.
(1)求
对所有的实数
成立的充要条件(用
表示);
(2)设
为两实数,
且
,若
,求证:
在区间
上的单调增区间的长度和为
(闭区间
的长度定义为
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e791569ccbc56a3fca4781c16965c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec09e7ab26188617083f3b467231250.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8c97a77335a5dc082b1e99154eee37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3c5a4887dfe02b02ee90d740151e1d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f92ba9f2cf267c946ff378c0a21f3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ffcddd15cefbf62ef3b3cb40b0cc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
2016-11-30更新
|
1691次组卷
|
3卷引用:2008年普通高等学校招生全国统一考试数学试题(江苏卷)