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Big O Notation

  1. Feb 20, 2006 #1
    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?
  2. jcsd
  3. Feb 20, 2006 #2


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    Well, starting with the definition of "O" would be a good idea. What is it?
  4. Feb 20, 2006 #3

    I'm able to determine n in simpler cases, but I have no idea how to approach the root of this polynomial.
  5. Feb 20, 2006 #4


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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. Feb 20, 2006 #5
    Err, typing this stuff out is difficult. Here's an example with polynomials: http://en.wikipedia.org/wiki/Big-O_notation#Example . It's images so it's easy to read.
  7. Feb 21, 2006 #6


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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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