2023高三·全国·专题练习
解题方法
1 . 人们很早以前就开始探索高次方程的数值求解问题.牛顿在《流数法》一书中,给出了高次代数方程的一种数值解法——牛顿法.这种求方程根的方法,在科学界已被广泛采用.例如求方程
的近似解,先用函数零点存在定理,令
,
,
,得
上存在零点,取
,牛顿用公式
反复迭代,以
作为
的近似解,迭代两次后计算得到的近似解为______ ;以
为初始区间,用二分法计算两次后,以最后一个区间的中点值作为方程的近似解,则近似解为______ .
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2 . 人们很早以前就开始探索高次方程的数值求解问题.牛顿在《流数法》一书中,给出了高次代数方程的一种数值解法——牛顿法.这种求方程根的方法,在科学界已被广泛采用,例如求方程
的近似解,先用函数零点存在定理,令
,
,
,得
上存在零点,取
,牛顿用公式
反复迭代,以
作为
的近似解,迭代两次后计筫得到的近似解为______ ;以
为初始区间,用二分法计算两次后,以最后一个区间的中点值作为方程的近似解,则近似解为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb11f2aa8ff8f92239dd208752700b.png)
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2023-05-10更新
|
523次组卷
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5卷引用:广西2023届高三毕业班高考模拟测试数学(理)试题
广西2023届高三毕业班高考模拟测试数学(理)试题辽宁省农村重点高中协作校2023届高三第三次模拟考试数学试题西藏林芝市2023届高三二模数学(理)试题(已下线)【一题多变】零点估计 牛顿切线(已下线)北师大版本模块五 专题4 全真能力模拟4(高二期中)
真题
解题方法
3 . 方程
的根![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb076d5aa58122b1f6a7501975a946d.png)
___________ .(结果精确到0.1)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb076d5aa58122b1f6a7501975a946d.png)
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2022-11-09更新
|
442次组卷
|
4卷引用:2003 年普通高等学校招生考试数学(理)试题(上海卷)
2003 年普通高等学校招生考试数学(理)试题(上海卷)2003 年普通高等学校招生考试数学(文)试题(上海卷)(已下线)考点13 函数的零点 2024届高考数学考点总动员(已下线)【第三课】4.5.1函数的零点与方程的解 4.5.2用二分法求方程的近似解
名校
4 . 令函数
,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
;……由此能得到一个数列
随着n的不断增大,
会越来越接近函数
的一个零在点
,因此我们可以用这种方法求
零点
的近似值.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___________ (快于、等于、慢于)二分法.
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5 . 中国古代近似计算方法源远流长,早在八世纪,我国著名数学家、天文学家张隧
法号:一行
为编制
大衍历
发明了一种近似计算的方法
二次插值算法
又称一行算法,牛顿也创造了此算法,但是比我国张隧晚了上千年
:对于函数
在
处的函数值分别为
,
,
,则在区间
上
可以用二次函数
来近似代替,其中
,
,
.若令
,
,
,请依据上述算法,估算
的近似值是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
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