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Math 104A Homework #2 Instructor: Lihui ChaiGeneral Instructions: Please write your homework papers neatly. You need to turn in bothfull printouts of your codes and the appropriate runs you made. Write your own code, individually.Do not copy codes!1. (a) Write the Lagrangian form. of the interpolating polynomial P2(x) corresponding to thedata in the table below:(b) Use P2(x) you obtained in (a) to approximate f(2).2. (optional) We proved in class thatkf Pnk1 (1 + n)kf P nk1; (1)where Pn is the interpolating polynomial of f at the nodes x0, ..., xn, P n is the best ap-proximation of f, in the maximum (in nity) norm, by a polynomial of degree at most n,is the Lebesgue constant (here the l(n)j are the elementary Lagrange polynomials).(a) Write a computer code to evaluate the Lebesgue functionassociated to a given set of pairwise distinct nodes x0, ..., xn.All course materials (class lectures and discussions, handouts, homework assignments, examinations, web ma-terials) and the intellectual content of the course itself are protected by United States Federal Copyright Law, theCalifornia Civil Code. The UC Policy 102.23 expressly prohibits students (and all other persons) from recordinglectures or discussions and from distributing or selling lectures notes and all other course materials without the prior(b) Consider the equidistributed points xj = 1 +j(2=n) for j = 0;:::;n. Write a computercode that uses (a) to evaluate and plot L(n)(x) (evaluate L(n)(x) at a large number ofpoints x to have a good plotting resolution, e.g. xk = 1 + k(2=ne), k = 0;:::;ne withne = 1000) for n = 4, 10, and 20. Estimate n for these three values of n.(c) Repeat (b) with the nodes given by xj = cos(j n ), j = 0;:::;n. Contrast the behavior. ofL(n)(x) and n with those corresponding to the equidistributed points in (b).3. (a) Implement the Barycentric Formula for evaluating the interpolating polynomial for arbi-trarily distributed nodes x0;:::;xn; you need to write a function or script. that computesthe barycentric weights (n)j = 1= k6=j(xj xk) rst and another code to use these valuesin the Barycentric Formula. Make sure to test your implementation.本团队核心人员组成主要包括BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：[email protected] 微信：codehelp QQ：99515681 或邮箱：[email protected] 微信：codehelp