Big O Notation

  • Thread starter hain
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  • #1
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I'm having some trouble with this discrete question:

Find the least natural number n such that
√(x² + x³ + 3) is O(xⁿ).

With the value of n that you have found, is it true that
xⁿ is O( √(x² + x³ + 3) )?


Can anyone help?
 

Answers and Replies

  • #2
HallsofIvy
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Well, starting with the definition of "O" would be a good idea. What is it?
 
  • #4
Hurkyl
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These are easy: they're close enough to polynomials for the purposes asymptotic analysis. How would you do it if it was a polynomial?
 
  • #6
HallsofIvy
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Why would you want to find a root? What is
[tex]\frac{\sqrt{x^2+x^3+ 3}}{x^n}[/tex]
?
 

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