function [y]=hw2_1_15(x, tol)

% given x and tol as input, calculate y=ln(1+x) using Talyor series to within
% tolerance tol

oldy=x;         % initial value of y (just the first term in the series)
y=oldy-x^2/2;   % add one more term so we can measure tolerance

k=2;            % we've used 2 terms so far

% add another term while tolerance is NOT less than tol
while (abs(y-oldy)>tol)
    k=k+1;      % next term
    oldy=y;     % remember the last value y then ... 
    y=oldy + (-1)^(k+1) * x^k / k;    % ... add another term
    
    % delete the percent sign below if you want to see the iterates of y
    % disp(y)
end
x
tol
disp('check the accuracy (these two results should be close)')
disp('actual')
disp(log(1+x))
disp('approximate')
disp(y)