名校
1 . 令
,对抛物线
,持续实施下面牛顿切线法的步骤:
在点
处作抛物线的切线,交x轴于
;
在点
处作抛物线的切线,交x轴于
;
在点
处作抛物线的切线,交x轴于
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
由此能得到一个数列
.
(1)设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506b899e000e05fe96a895aec315240b.png)
_____________ ;
(2)用二分法求方程
在区间
上的近似解,根据前4步结果比较,可以得到牛顿切线法的求解速度为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79446191602c1d2f941728ba8591b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9df2062940530232ab124a571e951ed.png)
在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb652143b43cc9439a347b2b1dc5cf6.png)
在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc47735cc385a3474bc1dabad322304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367304824e7eb354ffeb937fa209d80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
由此能得到一个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e201e8ef034040cea928961c5a8b6ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506b899e000e05fe96a895aec315240b.png)
(2)用二分法求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99606defee81cacc6652482953b6818c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
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