Question

Submission Items: (1) A Word document in which you: a. Describe in brief the problem you are solving and the numerical method used. b. Snapshot of the output, when you run the program for the conditions mentioned in the questions. c. Discuss your results. (2) MATLAB code (m) file() Question 1: [10 points) Write a MATLAB function that calculates the approximate value of arctan(x) using the Maclaurin series approximation: arctan(x) = x- + +... The function should accept 3 parameters: value of X, number of significant figures accuracy i.e. n, and the maximum number of iterations. In the function, use Es = (0.5 X 10-* % in order to continue until the Ea falls below this criteria. The function should return 3 values: the approximate value of arctan(x) at the end of the program, final Eq and the number of iterations it took Submit the snapshots showing the program running from the command prompt for x = 0.4 and 0.8, and plot Absolute true error vs. number of terms. Question 2: (10 points] Write a MATLAB function that uses Bisection Method to iteratively estimate the positive real root of the equation In(x) -0.7 in the interval [xl, xx] until Ea is less than es. Note that x is in radians. The function should accept 3 parameters: initial xi, Xx and Es, and return these 5 parameters for each iteration: X, X, X Sign{f(x)f(x)) and Ea (Hint: Function should retum arrays instead of single values). Please write a script which gives output in the following tabular form for the developed function using X, = 0.5, X-2 and es = 0.1%. Submit the snapshot of the output of the script. Iteration X L XXL Sign{f(xf (x)} Ed(in ) 0

Answer 1

`Hey,

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1)

clc%clears screen
clear all%clears history
close all%closes all files
[S,ea,i]=arctan(0.4,6,100)
[S,ea,i]=arctan(0.8,6,100)

function [S,ea,i]=arctan(x,n,imax)
S=0;
prev=0;
for i=1:imax
S=prev+(-1)^(i-1)*x.^(2*i-1)/(2*i-1);
if(abs((S-prev)/S)<0.5*10^(2-n))
break;
end
prev=S;
end
ea=abs((S-prev)/S);
end

- O X Pradeep EDITOR PUBLISH VIEW do E C . Search Documentation Insert fx Comment % 92% Indent 1 - EDIT Run Section Advance Breakpoints EL Run and Advance Run Aduan Run and Time BREAKPOINTS RUN ох HomeworkLib2.m x testc. mx eulerSystem. m x ahk. m x nse_filt. m x + MATLAB R2018a HOME PLOTS APPS D E L Find Files 3 Compare - New Open Go To - Save Print Find FILE NAVIGATE a Windows System32 Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Editor - C:\Users\PRADEEP KALRA\Documents\MATLAB\saveee.m +1 saveee. mx bisectionmethodbypradeep.m x googleLinks. m x for i=1:imax S-prev+(-1)^(i-1) *x. (2*1-1)/(2*1-1); if (abs ((S-prev)/S) <0.5*10* (2-n)) break; end prev=S; end ea=abs((S-prev)/S); end IIIIIIIII Command Window Details 0.6747 Workspace Name Value 4.7348e-05 4.7348e-05 Es 0.6747 fx >> arctan In 17 Col 4 ENG 1:59 PM IN 02/29/20 = Type here to search

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