which grows faster as x--> infinity? ln(x^2+4) or x-5? so using L'H rule i got lim as x-->infinity of [ln(x2+4)]/(x-5) = [2x/(x2+4)]/1 = 2x/(x2+4) then using L'H rule again i got 2/2x, then again i 0/2 = 0. So, does that mean that x-5 grows faster? And why?