function fx = maclaurin2(x,Ea_desired)

%MACLAURIN approximates log(1+x/1-x) using the MacLaurin series expansion
%
%   (this section is skipped to avoid giving away part of the solution)
%
%   Inputs:
%      X: a scalar with -1 < X < 1
%      EA_DESIRED: a scalar with the desired approximate error
%
%   Output:
%      FX: a scalar containing the MacLaurin approximation 
%
%   Assumptions: 
%         - the input is inside the interval (-1,1)
%         - the desired approximate error is strictly positive
% check whether the input is valid
if length(x)>1
    error('function only works for scalars');
end
if abs(x)>=1
    error('abs(x) must be smaller than 1');
end

max_iter = 1000;
fx = 2*x;
x_power = x;
for i=2:max_iter
    x_power = x_power*x*x;
    new_term = 2/(2*i-1)*x_power;
    fx = fx+new_term;
    % check whether we have reached the desired accuracy
    if (abs(new_term) < abs(Ea_desired))
        return;
    end
end
% this should only occur if the maximum number of iterations has
% been exceeded
warning('the approximation does not satisfy the desired accuracy')
return;