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Math Help - Determining the order of a function with big Oh

  1. #1
    Junior Member
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    Determining the order of a function with big Oh

    I was wondering if anyone could double check my answers below please.

    Give the order of the following functions,

    1. Ta(n) = 20^2 + (n + 4)^3
    2. Tb(n) = (6n + 4)^2 + 3nlog2(n)
    3. Tc(n) = (7n + 1)^2log10(n)

    I got the following orders:-

    1. \theta(n^2)
    2. \theta(n log n)
    3. \theta(log n)

    Item 3 is the most effecient for very large values of n.
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  2. #2
    Member mohammadfawaz's Avatar
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    Lebanon - Beirut
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    1) the expression of the third order since it contains n^3 which dominates the whole expression, hence you get \theta(n^3)
    2) you have a part which is of the second order: n^2 and another one of order nlog_{2}(n) which is lower than n^2 hence the total order is \theta(n^2)
    3) Here, you have multiplication of a polynomial of the second order with log_{10}(n) hence the order is \theta(n^2log_{10}(n))

    Clearly, the most efficient is the second one since n^2 < n^2log_{10}(n) < n^3
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