名校
解题方法
1 . 已知
是数列
的前n项和,
是以1为首项1为公差的等差数列.
(1)求
的表达式和数列
的通项公式;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c09815106a2134d1699906e44228061.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b9c9cea7a8730189fbe1b1d70e7fd2.png)
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2 . 函数
的单调递减区间是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4964c3c4b7e5863d25f382f75cd5bad.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知
,关于x的方程
有三个不同实数根,则m的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f26a43391746dad0500b7919f25cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55d8ea498c2c1b4e21bb10d274e9518.png)
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4 . 已知
在
处取得极大值1,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df31cd25f8d79d292b16d12c9dca36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
A.![]() | B.对称中心为![]() |
C.![]() | D.![]() |
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解题方法
5 . 数列
满足
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdd1883cc87c87dbc38f64c8d98e716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b37aad30364ba61218231d58ac0274d.png)
A.2565 | B.2575 | C.2585 | D.2595 |
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解题方法
6 . 已知函数
,
,若
,且关于x不等式
在
上恒成立,其中e是自然对数的底数,则m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e16b4509adc82a16d798aecab1a8f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb4c86e61ca983ffcaad2cd28284fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82660976e3c0e1f31d8ba05bf4ef1f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 已知
,若
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfc436eb1738984ed3b50eca6569a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ea41f2dd03bed1c50167eef87a42ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
A.0 | B.1 | C.e | D.2e |
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8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559447f0f9d01acba3d220d9b6b90383.png)
(1)当
时,求
在
处的切线方程.
(2)设
分别为
的极大值点和极小值点,记
,
;
①证明:直线
与曲线
交于另一个点C;
②在①的条件下,判断是否存在常数
,使得
,若存在,求n;若不存在,说明理由.
附:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559447f0f9d01acba3d220d9b6b90383.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6470c6a4349ea591ce2bbcd93199f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d14d55cbbfe1f2b82c41efcae8efad1.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②在①的条件下,判断是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0723ba7f3a8721cb1381d5be9dc12447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357924c44549675683398a0b7c9bcb26.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b7cfcc147916ae7eeb5d557fea945e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d90807e6a0085068ae47a101b7c87d6.png)
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9 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)讨论
的单调性;
(2)若函数
在闭区间
上的最大值为
,求a的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f534e406c9469126bf57fd912f778925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30df669b0dc941afa96996ea96e09433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c075da55da267355e0d9ab332eb2f76f.png)
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10 . 下列判断正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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