title: How to arrange the functions in the order of growth rate? So that f(n) is O(g(n))
body: <p>I have the below functions that needs to be ordered in their growth rate. But how can we show that the function g(n) immediately follows function f(n) in the list, then it should be the case that f(n) is O(g(n))?</p>
  
  <p><a href="https://i.stack.imgur.com/N3S1Z.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/N3S1Z.png" alt="functions"></a></p>
  
  <p>I tried by key-in some values for n (such as 10, 1000, 5000) and it is coming as 5 &lt; 4 &lt; 2 &lt; 1 &lt; 3, from 1000.</p>
  
  <p>How can I prove this order asymptotically?</p>