In Matlab code A common (but not efficient) Taylor series expansion lets us appr

Question

In Matlab code

A common (but not efficient) Taylor series expansion lets us approximate the arctangent function using tan^-1(x) = sigma_n=0^m (-1)^n x^2n+1/2n+1 which has m+1 terms and is valid for x in [-1, 1]. The approximation becomes exact as m rightarrow infinity. Write a Matlab script that prompts the user for x and the highest order term, m and reports the approximated value of arctan(x) using a counting (for) loop. Note that, since the tangent of pi/4 (45 degree) is 1, we can use 4 tan^-1(x) = pi as an easy check on how close the approximation is getting. Of course, it is also easy to check using a calculator or Matlab's atan function. (The filename should be hw06_02. m.)

Explanation / Answer

Matlab Code:

x=input('Enter the value of x: ');
m=input('Enter the value of m: ');
sum=x;
for i=1:m
sum=sum+(((-1)^i)*(x^(2*i+1)))/(2*i+1);
end
disp(sum);
disp(atan(x));

Output:

Enter the value of x: 1
Enter the value of m: 100
0.7879

0.7854

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