设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb03b3a9fe5da30c791ce4abcecf02b.png)
.
(1)化简:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84596f2f873602967ac204a0921b601.png)
;
(2)已知:
,求
的表达式;
(3)
,请用数学归纳法证明不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb03b3a9fe5da30c791ce4abcecf02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfe0778f3d1edc7756a4b8c51e5c1bc.png)
(1)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84596f2f873602967ac204a0921b601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfe0778f3d1edc7756a4b8c51e5c1bc.png)
(2)已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcda62e52eed905e59881e926996935d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb10cebd5e38daaf05305bdcf68b8d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632dfb2eef3413e17ea5f12b0a7ecece.png)
更新时间:2019-09-08 11:15:26
|
相似题推荐
解答题-证明题
|
较难
(0.4)
名校
【推荐1】对于给定的函数
,定义如下:
其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c7aab4df25884973273efae244f2df.png)
(1)当
时,求证:
;
(2)当
时,比较
与
的大小
(3)当
时,求
的不为
的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729065c88ccb1ca1071319a4dfb04fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c7aab4df25884973273efae244f2df.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5d30d6d24314d9d2925cdc33b04815.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bfbf2be4f1b96be108b9c1b7e82262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed70ca50c63a55128f61af3e3ac8f453.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
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解题方法
【推荐2】若函数
的定义域、值域都是有限集合
,
,则定义
为集合A上的有限完整函数.已知
是定义在有限集合
上的有限完整函数.
(1)求
的最大值;
(2)当
时,均有
,求满足条件的
的个数;
(3)对于集合M上的有限完整函数
,定义“闭环函数”如下:
,对
,且
,
.若
,
,
,则称
为“m阶闭环函数”.证明:存在一个闭环函数
既是3阶闭环函数,也是4阶闭环函数(用列表法表示
的函数关系).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d677b98bf6b39322ba1be58a4def3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.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/47eed557063f07462d7dbe78da5ec3e2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb29bacf2fcc07be37f89f9ad7a7faf.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6032aee742b136f8ea08073426fcb2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d1ff786e39d2fce9e79a2ea3e969e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(3)对于集合M上的有限完整函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39e176af5b23719580d925e792aa8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c88248a34d270530f9d01570a911878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7149bd8132fd52cec51ae0f29986157a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c15f41c30653e445108fe7d3d8aa0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f29c06a3e9a73e905eb87d71efa201c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd09c401bb5423fb9272cad59a5e079a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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【推荐1】请阅读:当
时,在等式
的两边对
求导,得
,利用上述方法,试由等式
(
,正整数
).
(1)证明:
;(注:
)
(2)求
;
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96197741cee878c94318b9d840b46a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c78795768ff8d31eb51ec0b17f9f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d7664675da7c27b90e54cb7887eb2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd19918a18603b334b3faa77f2b2ace2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82add3c2f480d0c092f497a32c6da3e9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc9b7fa551545192e12b1371f34de05.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3772441403ffd20d525b6b529a5108d7.png)
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【推荐2】已知数列
满足
且
,设
,
.
(1)求
;
(2)求
的通项公式;
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fe02eafd69ba8fc70667c3c3627369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1179414a71459a3cfa134ace94302e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5778e58cc647a85d4a76be9689f7fdf.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2b897be2d8d0f0388758492792f7cb.png)
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