Mathematics - Limits Question with Solution | TestHub

Let $y=f(x)$ and $z=\sqrt{x-\sqrt{x+\sqrt{x-\cdots }}}$. Then $y^2=x+z,z^2=x-y$, and hence $y-z=1$. Thus $y=(1+\sqrt{4x-3})/2$. Substitution and rationalisation give the limit 3/4.