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Math Help - Big O examples

  1. #1
    Junior Member
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    Big O examples

    Hi didn't really know where this belongs so here goes...

    show that log_eN^c=O(N) \forall c \in \mathbb{R}\setminus{0}

    and

    find O(f(x)) for f(x) = x^4 + 2^x + log_en

    Thanks a lot for the help all=)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by james12 View Post
    Hi didn't really know where this belongs so here goes...

    show that \log_eN^c=O(N) \forall c \in \mathbb{R}\setminus{0}
    \log(N^c)=c\log(N)

    Then as \log(N) \in O(N), so is c\log(N).

    If you need to prove that: \log(N) \in O(N)
    you use L'Hopital's rule to show that:

    \displaystyle \lim_{N \to \infty} \frac{\log(N)}{N}=0

    and the result follows from that.

    CB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by james12 View Post

    find O(f(x)) for f(x) = x^4 + 2^x + log_e x
    As:

    \displaystyle \lim_{x \to \infty} \frac{x^4}{2^x}=0

    and

    \displaystyle \lim_{x \to \infty} \frac{\log_e(x)}{2^x}=0

    we can conclude:

    f(x) \in O(2^x)

    CB
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  4. #4
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    Thanks so much CaptainBlack, life saver=) =)
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