Problem 2-Modify textbook problem 4.11 (both editions) by evaluating the followi

Question

Problem 2-Modify textbook problem 4.11 (both editions) by evaluating the following function at x = 0.3. 2! 3! 4! Problem 3-Plot the function (x)-2x-x+4 for the interval [2, 2]. Determine the exact value of the first derivative of the function at x-1 using calculus method. Then, numerically determine the first derivative of the function at x=1 using forward, backward, and centered difference approximations with a step size of h=0.5. Compare the approximate derivatives with the exact value and comment on which of the three finite difference approximations is most accurate.

Explanation / Answer

Solution:

Executable code:

Matlab code:

clc

clear all

% FOR ITERATION

n1=1; % for iteration

c11=1:100;

% INITIALIZING 1ST VALUE USING MACLAURIAN SERIES

value(1)=((-1)^(1+1)*0.74^(2*1-1))/(2*1-1);

% PERCENTAGE ERROR

errorpercent(1)=abs((atan(0.74)-value(1))*100/atan(0.74));

while n1<100

n1=n1+1;

value(n1)=((-1)^(n1+1)*0.74^(2*n1-1))/(2*n1-1);

% SUMMATION ACCORDING TO MACLAURIAN SERIES FORMULA

value(n1)=value(n1-1)+value(n1);

errorpercent(n1)=abs((atan(0.74)-value(n1))*100/atan(0.74));

end

A=[c11;errorpercent;value];

fileIDs = fopen('result.txt','w');

fprintf(fileIDs,' N(ITERATION) PERCENTAGE ERROR VALUE ');

fprintf(fileIDs,'%d %6.2f %1.4f ',A);

fclose(fileIDs);

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