1 . 如图,在平面四边形
中,已知
分别是棱
的中点,若
,设
,则
的最大值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a337a934b801730321f67b0e5a0b144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207551e47a49ebdf447aab8cba24e560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0048a0a64059e3025b004671a1f1cbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5e3d14fb4911c1f590fe518df1fa4b.png)
![](https://img.xkw.com/dksih/QBM/2016/11/9/1573135574802432/1573135581093888/STEM/691841b9b8c94b31b31320742ac01ab3.png?resizew=260)
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2 . 如图,已知曲线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497aceb0440d794dfedf2cdd42e131ce.png)
及曲线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc9e65f2fa9af923d5db7cff37782d7.png)
,
上的点
的横坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
.从
上的点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
作直线平行于
轴,交曲线
于点
,再从点
作直线平行于
轴,交曲线
于点
,点
(
,2,3……)的横坐标构成数列
.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572525822836736/1572525829177344/STEM/b12a6ba397f64d30b29f8afd385551f4.png?resizew=246)
(1)试求
与
之间的关系,并证明:
;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497aceb0440d794dfedf2cdd42e131ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc9e65f2fa9af923d5db7cff37782d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9993f6dc979bfbe11ca160daf225d6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79dc80683f49c71b505e4bb711dbbb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572525822836736/1572525829177344/STEM/b12a6ba397f64d30b29f8afd385551f4.png?resizew=246)
(1)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e22720a7250e79903635cb6eb368b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265ec3d91f1abd3cb756888d21ee7ae3.png)
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3 . 已知
,且
,
1,2,3,….
(1)求
,
,
;
(2)求数列
的通项公式;
(3)当
且
时,证明:对任意
都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6239ed3841d978597c9ceccad39f34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51018950f47e4f7e216989a3d765ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba590f71638ebfbb77e4c1d7bdb64a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b993b03b702b2f8f0296d7c6d1ce3775.png)
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