解题方法
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7f673cf793364aad2543ee8ae06228.png)
(1)请在网格纸中画出
的简图,并写出函数的单调区间(无需证明);
(2)定义函数
在定义域内的
,若满足
,则称
为函数
的一阶不动点,简称不动点;若满足
,则称
为函数
的二阶不动点,简称稳定点.
①求函数
的不动点;
②求函数
的稳定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7f673cf793364aad2543ee8ae06228.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/3dd251f6-1acf-44cf-b925-66705e04e25c.png?resizew=210)
(1)请在网格纸中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)定义函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de4841073ba41dc0e7b976759c3cd4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52dc0a7f95a39091a2f11d80cc8579f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a576aa37d6f504669b40b7b38cb92694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
②求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
您最近一年使用:0次
2 . 已知:底与腰之比为
的等腰三角形为黄金三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d906e69c-33ad-47c1-87a1-046eb54ce27b.png?resizew=337)
(1)如图1,
即为黄金三角形尺规作图.已知
,求
长为______,
为______.
(2)如图2,即为正五边形尺规作图.求证:五边形
(所作图形)即为正五边形.
(3)请用另一种方法尺规作图作出正五边形.简要叙述作图方法,无需作图.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d906e69c-33ad-47c1-87a1-046eb54ce27b.png?resizew=337)
(1)如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
(2)如图2,即为正五边形尺规作图.求证:五边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
(3)请用另一种方法尺规作图作出正五边形.简要叙述作图方法,无需作图.
您最近一年使用:0次
3 . 已知函数
,数列
分别满足
,且
. 定义
,
为实数
的整数部分,
为小数部分,且
.
(1)分别求
的通项公式;
(2)记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddb9f59ac6af99a8e1db5c320b47fe0.png)
,求数列
的前项
和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c07bd1bced5e02c11b99392f9526f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9228e116fa73d185ec844123fb9ca281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28fd5938f16b0ce8b51a74739d0e062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0838b3fea2e2f365b9c0deab6a9678ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921500908058bb0e7c170a35fb70fc00.png)
(1)分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddb9f59ac6af99a8e1db5c320b47fe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b5b5a40ce9e5f2a8cab8b9a7f36b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2016-12-04更新
|
792次组卷
|
3卷引用:第十三届高一试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)