解题方法
1 . 已知函数
满足下列条件:
(1)当
时,
,且
;
(2)当
时,
;
(3)在
上的最小值为0.
求最大的
,使得存在
,只要
,就有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7620b8fd2fe76cdcfceee953e1492e90.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd089822beae382e173954e7b2f5b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f028e597d34316db2c4c993fc72ff32d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff133c17652425c22f0b367e002797df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda178cf86d2baff95be7e655f020fc3.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
求最大的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884ce1e9436d39f34f6d3116cb2a140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08696f29924fad88f81c45c11149917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa5db87f46602bdba3df300ffe16b0a.png)
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解题方法
2 . 平面向量
,若存在整数
使
,且
,试求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a4521f0658e021ad28318d8db27426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09737e117adb481fd3c4affdf38ff45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245d4ac7e6c91f3ea4028bdeb2fb1a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f92ffd4c85efa2d4a1692459a06cbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bdb686910f213670f2c6f9e46c1f62.png)
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3 . 已知
,若
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a0a06e7b4c16d25801029ba90c887e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0f24d1daf9447a4837e7886261c592.png)
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4 . 实数列
满足
为
前k项和,令
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4479bae6c067537f99bd8a74b69efb5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b823bb30ecbe7ea3a48e35d16cf0d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c00f1e8a107981c5b654608f55e0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f89080740f515f64a5077647b3ca927.png)
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解题方法
5 . 已知
(其中a,b为常数,且
)在
上的最大值和最小值分别为
和
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200dd30171e6c5895abbda91d0e9d195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b172723002461ae60798317e2f10f6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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解题方法
6 . 已知
对任意
,有
,若
,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ee0bd8a541d6c1057325f7f4287a64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa130b80a64f150b2ab78d40cf128c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985c6ed2a37efcbc1718590a4277e278.png)
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解题方法
7 . 数列
满足
,且
.
(1)求
;
(2)是否存在实数
,使得
,且
为等差数列?若存在,求出
的值;若不存在,说明理由.
(3)求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336d7c50da66b232b05f04dad2be86c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff473e6f6c537d98b685a78d077f850.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfffff86bd7b4fc94294ac13d767d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
8 . 已知函数
满足:①
;②
.
(1)求
的解析式;
(2)若对任意的实数
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151d298dfc870b6b18cdaae71f0ec58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b5320a6f673d6c2e70a815adaf2440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3b0265cf54af7f995a8077631c05f5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ca61ca3fd4d22d326aa8cbda82dca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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9 . 已知集合
,
(1)若
,求实数
的值;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7739501d4e2196e1d10f6e1b91e18b26.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc992c9e51d4b22232adf6bb5c8055a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9d50619b779c1056602f46b2a95e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 过曲线
:
上的点
作曲线
的切线
与曲线
交于
,过点
作曲线
的切线
与曲线
交于点
,依此类推,可得到点列:
,已知
.
(1)求点
,
的坐标;
(2)求数列
的通项公式;
(3)记点
到直线
(即直线
)的距离为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51443d97c22cfa55a47270bfdd7b37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f724c379a00959905b87eedbe6d61fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(3)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f04dcabdafec74f98f4a1f4faa3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91321f9e0b712ccef47c4b9e0baca333.png)
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