In a head-on, proton-proton collision, the ratio of kinetic energy in the center of mass system to the incident kinetic energy is $$R = \frac{\sqrt{2mc^2(E+2mc^2)}-2mc^2}{E}.$$

Approximate $R$ with the first two nonzero terms of the Taylor series when $E << mc^2$ (i.e. in the nonrelativistic scenario):
$R\approx$ .

Approximate $R$ with the first two nonzero terms of the Taylor series when $E >> mc^2$ (i.e. in the extremely relativistic scenario):
$R\approx$ .

(Hint: If $x >> y$, then $\frac{y}{x} \approx 0$.)