How many iterations to get accuracy within $10^{-8}$
$g(x)= 1/3\cdot\ln(2-x^2)$ when $x_0=0.5$ I used $|0.186539-0.5|\cdot{\lambda}^{n}/(1-\lambda) $ where $\lambda = 2/3$ and got $n \geq 46$
but I smell a mistake.
Note: the original question is $f(x)= e^{3x}+x^2-2$, does it converge to zero $\alpha \in (0,1)$ for any $x_0\in(0,1)$
