21-22高一·全国·课后作业
1 . (1)二分法的概念
对于在区间
上图象连续不断且
的函数
,通过不断地把它的______________________ 所在区间___________ ,使所得区间的两个___________ 逐步逼近零点,进而得到零点近似值的方法叫做二分法.
(2)用二分法求函数零点近似值的步骤
给定精确度
,用二分法求函数
零点
的近似值的一般步骤如下:
①确定零点
的初始区间
,验证
.
②求区间
的中点c.
③计算
,并进一步确定零点所在的区间:
a.若
(此时
),则c就是函数的零点.
b.若
(此时
),则令___________
.
c.若
(此时
,则令___________
.
④判断是否达到精确度
:若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4eb66ac6a2bb80ff78ce197bc78625.png)
___________ ,则得到零点近似值a(或b);否则重复步骤②~④.
对于在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd3c1b264eff8fe210ae2363ee22204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)用二分法求函数零点近似值的步骤
给定精确度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711c92626a97e6b778b3aa86e663ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
①确定零点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd3c1b264eff8fe210ae2363ee22204.png)
②求区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
③计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de447d5e47448d0f15a7535bf3ce0be.png)
a.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52060e238cf1e17a8101f2c47121c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d910e4fc95f2d5ae748a22cb90d9d723.png)
b.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86601f789cfe026058c89baa12fa26f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c2f8f034d05f233daef6d6fef6a10f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c30977edc1458a3b8f5acc0d9df1b5c.png)
c.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df124a3af22788f511439954d7b6c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ddf24617e6bcd7460876f8dad700c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c30977edc1458a3b8f5acc0d9df1b5c.png)
④判断是否达到精确度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711c92626a97e6b778b3aa86e663ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4eb66ac6a2bb80ff78ce197bc78625.png)
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