高斯是德国著名的数学家,近代数学奠基者之一,享有“数学王子”的美誉,用其名字命名的“高斯函数”:设
,用
表示不超过x的最大整数,则
称为高斯函数,也称取整函数,例如:
,
,已知
,则函数
的值域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
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更新时间:2022-07-22 12:41:02
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解题方法
【推荐1】函数
的值域为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9faa22d5800e4a65f8b23827f56b3017.png)
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【推荐2】给出下列四种说法:(1)函数
(
,
)与函数
的定义域相同;(2)函数
与函数
互为反函数;(3)函数
的单调增区间是
;(4)函数
的值域为
.其中所有正确的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
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【推荐1】已知集合
.给定一个函数
,定义集合
,若
对任意的
成立,则称该函数具有性质“
”.现给出下列函数:①
;②
;③
,其中具有性质“
”的函数的序号是____________ (写出所有正确答案的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15435ce3ac7c9cba8c9fee03aefa3dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
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【推荐2】牛顿迭代法(
)是牛顿在17世纪提出的一种近似求方程根的方法.如图,设
是
的根,选取
作为
初始近似值,过点
作曲线
的切线
,
与
轴的交点的横坐标
,称
是
的一次近似值,过点
作曲线
的切线,则该切线与
轴的交点的横坐标为
,称
是
的二次近似值.重复以上过程,得到
的近似值序列.
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629415692427264/2632467863396352/STEM/7bc20668-1e0c-4b84-90b0-b114fa9828d4.png?resizew=445)
(1)请选出r的
次近似值与
的
次近似值的关系式______ (请填正确的关系式序号).
①
; ②
;
③
.
(2)若
,取
作为
的初始近似值,试求
的正根的二次近似值______ (请用分数做答).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1632303a4d32c717c95a4f5eb4e82cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506ec9e230c598077d1e68dba3db0a22.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629415692427264/2632467863396352/STEM/7bc20668-1e0c-4b84-90b0-b114fa9828d4.png?resizew=445)
(1)请选出r的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b597da47656808bcd5fd9bb991e72143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6507529acc3f1749d1f923c700ae8cb3.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8073e22879a01280bd4480636658af4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9eb2c259d27740f0ebb428444a0605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5603d29560e66b2293cea1e3b02289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
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