title: how do you prove that the big theta of a series is its leading term?
body: <p>if f(x) = (An) x^n + (An-1) x^(n-1) +...+ (A1)x + (A0)
  how can you prove f(x) is big theta(x^n).</p>
  
  <p>I've thought about it and one could do it by proving that f(x) big O(x^n) and x^n big O(f(x)). I've figured out the proof for the former (using triangle inequality) but could not understand how to do the latter.</p>
  
  <p>Alternatively one could prove f(x) is big omega (x^n).</p>
  
  <p>I've gotten stuck on this question and any hints or clues you could give me would greatly help.</p>