function fx = maclaurin(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_order = 2000;
new_term = Inf;
fx = 0;
i = 1;
while (abs(new_term) >= abs(Ea_desired)) && (i<max_order)
    new_term = 2/i*x^i;
    fx = fx+new_term;
    i = i+2;
end

if i>max_order
    warning('the approximation does not satisfy the desired accuracy')
end
return;