名校
解题方法
1 . 已知函数
.
(1)若
对任意的
恒成立,求t的取值范围;
(2)设
且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a570f4d94afa695d32548dda63a0e8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91011caeec60187fe2fc4e66310dd56d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2514db2de125390f82b1604143d0827c.png)
您最近一年使用:0次
2023-11-10更新
|
587次组卷
|
2卷引用:辽宁省大连市金州高级中学2023-2024学年高三上学期期中考试数学试题
名校
2 . 已知数列
各项不为0,前
项和为
.
(1)若
,
,求数列
的通项公式;
(2)在(1)的条件下,已知
,分别求
和
的表达式;
(3)证明:
是等差数列的充要条件是:对任意
,都有:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d47c7e11d66c03afa6f6af0e2add53e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在(1)的条件下,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c775e59822f942919fdda98704738957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9e976cab79185869e4283e1b487a07.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5134d5aa449a44c374d7cdbb6d94fe4d.png)
您最近一年使用:0次
3 . 已知
、
是函数
的图象上的任意两点,点
在直线
上,且
.
(1)求
的值及
的值;
(2)已知
,当
时,
,设
,
数列
的前
项和,若存在 正整数
,
,使得不等式
成立,求
和
的值;
(3)在(2)的条件下,设
,求所有可能的乘积
的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ebcde3bc579cc3e31c9fe7c1ae3e032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e43f2bfcbef70a5a6e19ef792fa60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c72bc49a2eafb73fb3297e1304923c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a21434554a6b14633fd06e3186e7c0e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6e75677951ef1388f76aee5a779149.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d33d9dd40d026e06bc3970d29db9bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7875482ed1d2b2f82bd2d8f1df8bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5310457751b485a5312fb78fca8a6dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07404ab51f404f9411f79bd4f1fde654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e81078b69a93798f4451f6ef3f764a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e5849ca5126de3399c78e9ef3ba753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bb9839c329dc48b68017050994478e.png)
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