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Math Help - Growth

  1. #1
    Newbie
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    Growth

    I have come accross a question which i cant get my head around, but i am guessing it is to do with groth and big o notation?

    Could some on point me in the right direction for finding some online material to learn this type of maths? as im lost with it!


    Consider the functions

    "f1(x) = x3 +3x2 +2x+1 and f2(x) = x4 +12x3 +7x2 +2x+1.
    What is the smallest value of m in N such that
    f1(x)+ f2(x) ∈ O(xm)?

    Justify your answer briefly."

    Many Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mrcheese View Post
    I have come accross a question which i cant get my head around, but i am guessing it is to do with groth and big o notation?

    Could some on point me in the right direction for finding some online material to learn this type of maths? as im lost with it!


    Consider the functions

    "f1(x) = x3 +3x2 +2x+1 and f2(x) = x4 +12x3 +7x2 +2x+1.
    What is the smallest value of m in N such that
    f1(x)+ f2(x) ∈ O(xm)?

    Justify your answer briefly."

    Many Thanks
    f_1(x)+f_2(x) is a quartic so eventually all the terms other than the one in x^4 become negligible compared x^4 so:

    f_1(x)+f_2(x)=O(x^4)

    To show that 4 is the least positive integer for which:

    f_1(x)+f_2(x)=O(x^m)\

    suppose m=3 that tells us that for x sufficiently large there exists a k>0:

    |f_1(x)+f_2(x)|<k x^m

    But as f_1(x)+f_2(x) is a quartic:

    \frac{f_1(x)+f_2(x)}{x^4}\le k x^{-1}

    But the left hand side tends to a finite limit as x \to \infty while the right hand side goes to 0... etc ... etc

    CB
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