Solution to 70 et 71 respectively:
I don't understand why we know $|y/(x^2+1)|$ <= |y| in problem 70. I think $|y/(x^2+1)|$ <= |y+x| is actually the case then let delta be half of .05.
I don't know how we knew that $|x+y/(x^2+1)|$ $<=|x+y|$ rather than $|x+y/(x^2+1)|$ $<=|y|$ in the solution of problem 71 and let delta be .01.
$$x^2 \geqslant 0 \Rightarrow x^2+1 \geqslant 1 \Rightarrow \frac{1}{x^2+1} \leqslant 1 \Rightarrow \frac{|y|}{x^2+1} \leqslant |y| $$
The same inequality is also used in the second example.