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Math Help - Calculation with Big Oh or Theta

  1. #1
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    Calculation with Big Oh or Theta

    I'm dealing with calculation in terms of Big Oh or Theta notations.

    For example,

    If I want to simplify O(n^k * sqrt ( a* n^m - n^p )) as much as possible, where a is positive constant and k,m,p are positive unknown, then is it possible for me to remove the term n^p?

    Then, the final answer is O(n^k * sqrt (n^m)). Is this correct?
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  2. #2
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    If I want to simplify O(n^k * sqrt ( a* n^m - n^p )) as much as possible, where a is positive constant and k,m,p are positive unknown
    Is there a difference between a constant and an unknown in this context?

    Then, the final answer is O(n^k * sqrt (n^m)). Is this correct?
    Yes. I would write it as n^{k + m/2}.
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  3. #3
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    Thanks for your reply.

    I think there is difference. If a is not constant, i.e., function of n, then a cannot be just cancelled... Anyway, I think a is not really important in my original problem.
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