Order functions by growth rate

EDIT: I’ve revised my answer based on the comments

I’ve got this HW question which asks me to order a list of functions by their growth rate. The question also asks to indicate which ones have the same growth rate. Here are the functions:

  • N
  • sqrt(N)
  • N^1.5
  • N^2
  • N log N
  • N log log N
  • N log^2(N)
  • N log(N^2)
  • 2/N
  • 2^N
  • 2^(N/2)
  • 37
  • N^3
  • N^2logN

And here is my answer. Bolded functions are what I think are the same:

  • 37
  • sqrt(N)
  • N^1.5
  • N
  • N log log N
  • N log N
  • N log^2(N)
  • N log (N^2)
  • N^2 log N
  • N^2
  • N^3
  • 2^(N/2)
  • 2^(N)
  • 2/N

This question is really confusing me. Is my answer correct? I used Wolfram Alpha to graph the functions, but comparing the growths got very complicated.

EDIT: My revised answer.

2/N, 37, sqrt(N), N^

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