2022年人教A版数学必修一3.1.2《用二分法求方程的近似解》导学案 .pdf

名师精编优秀教案3.1.2 用二分法求方程的近似解学习目标1.根据具体函数图象，能够借助计算器用二分法求相应方程的近似解；2.通过用二分法求方程的近似解，使学生体会函数零点与方程根之间的联系，初步形成用函数 观点处理问题的意识.学习过程一、课前准备（预习教材P89 P91，找出疑惑之处）复习 1：什么叫零点？零点的等价性？零点存在性定理？对于函数()yf x，我们把使的实数x叫做函数()yf x 的零点.方 程()0f x有 实数 根函 数()yf x的 图 象 与x轴函 数()yf x .如果函数()yf x 在区间 ,a b 上的图象是连续不断的一条曲线，并且有，那么，函数()yf x 在区间(,)a b 内有零点.复习 2：一元二次方程求根公式？三次方程？四次方程？二、新课导学 学习探究探究任务：二分法的思想及步骤问题：有12 个小球，质量均匀，只有一个是比别的球重的，你用天平称几次可以找出这个球的，要求次数越少越好.解法：第一次，两端各放个球，低的那一端一定有重球；第二次，两端各放个球，低的那一端一定有重球；第三次，两端各放个球，如果平衡，剩下的就是重球，否则，低的就是重球.思 考：以 上 的 方 法 其 实 这 就 是 一 种 二 分 法 的 思 想，采 用 类 似 的 方 法，如 何 求ln26yxx的零点所在区间？如何找出这个零点？新知：对于在区间 ,a b 上连续不断且()()f af bg0 的函数()yf x，通过不断的把函数的零点所在 的区间一分为二，使区间的两个端点逐步逼近零点，进而得到零点近似值的方法叫二分法(bisection).反思：给定精度，用二分法求函数()f x 的零点近似值的步骤如何呢？名师精编优秀教案确定区间 ,a b，验证()()0f af bg，给定 精度；求区间(,)a b 的中点1x；计算1()f x：若1()0f x，则1x 就是函数的零点；若1()()0f af xg，则令1bx（此时零点01(,)xa x）；若1()()0f xf bg，则令1ax（此时零点01(,)xx b）；判断是否达到精度；即若|ab，则得到零点零点值a（或b）；否则重复步骤 典型例题例 1 借助计算器或计算机，利用二分法求方程237xx的近似解.变式：求方程237xx的根大致所在区间.动手试试练 1.求方程3log3xx的解的个 数及其大致所在区间.文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 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ZW10Y3G7J9W4名师精编优秀教案练 2.求函数32()22f xxxx的一个正数零点（精确到0.1）零点所在区间中点函数值符号区间长度练 3.用二分法求33 的近似值.三、总结提升 学习小结 二分法的概念；二分法步骤；二分法思想.知识拓展高次多项式方程公式解的探索史料在十 六世纪，已找到了三次和四次函数的求根公式，但对于高于4 次的函数，类似的努力却一直没有成功，到了十九世纪，根据阿贝尔（Abel）和伽罗瓦（Galois）的研究，人们认识到高于4 次的代数方程不存在求根公式，亦即，不存在用四则运算及根号表示的一般的公式解 同时，即使对于3 次和 4 次的代数方程，其公式解的表示也相当复杂，一般来讲并不适宜作具体计算因此对于高次多项式函数及其它的一些函数，有必要寻求其零点近似解的方法，这是一个在计算数学中十分重要的课题.学习评价 自我评价你完成本节导学案的情况为（）.A.很好 B.较好 C.一般 D.较差 当堂检测（时量：5 分钟满分：10 分）计分：1.若函数()f x 在区间,a b 上为减函数，则()f x 在,a b 上（）.A.至少有一个零点 B.只有一个零点C.没有零点 D.至多有一个零点2.下列函数图象与x轴均有交点，其中不能用二分法求函数零点近似值的是（）.文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 ZW10Y3G7J9W4文档编码:CW6H4I7A5P6 HK2M7F6V7F5 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