I was wondering how fast x! grows as it approaches infinity as compared to x2, 2x, and xx. The last one was fairly obvious since x*x*x*x... > x(x-1)(x-2)(x-3)... But I can't figure out a way to show that x! grows faster than x2 or 2x. I know it grows faster since I can compare the graphs of the functions on my calculator but I want to understand why. This since it seems like it would be helpful in solving limits where x approaches infinity, and using the comparison test for series which involve factorials.