Which grows faster as x tends to infinity, (x-4)3 or 2x3 + ln(x)? Steps: 1) lim (x-4)3/[2x3 + ln(x)] 2) The limit is infinity/infinity as x tends to infinity, so we can use L'H rule. 3) Applying L'H rule we get [3x(x-4)2]/(6x3 + 1) 4) The limit is again infinity/infinity as the above function tends to infinity, so we apply L'H again. 5) Applying L'H rule we get [3(x-4)(3x-4)]/18x, which yet again yields infinity/infinity as x tends to infinity, so, we apply L'H rule again. 6) Applying L'H rule we get (18x-48)/18 which is equal to infinity/18 = infinity. Solution: (x-4)3 grows faster because the limit approaches infinity. I know i did something wrong because the answer is that they grow at the same rate. Can anyone point out my mistake(s)? Thanks!