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Math Help - Big-O notation question

  1. #1
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    Big-O notation question

    hi guys,
    can someone pls explain big-o notation to me in easy to understand way with an easy example?? I am trying to understand it by reading my textbook but i am not getting it at all. It uses the following example: show that f(x) = x^2 + 2x + 1 is O(x^2)

    My first question is, what value of x do i start with?? i dont know how one chooses a value of x to start with. in the book, it starts with x > 1. I dont understand how they came up with 1 instead of 2, 3 or any other number.

    if someone could please answer my question and also explain the big-o notation in an easy to understand way with an example, it would be great. thanks a lot in advance! i really appriciate it.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bokasoka View Post
    hi guys,
    can someone pls explain big-o notation to me in easy to understand way with an easy example?? I am trying to understand it by reading my textbook but i am not getting it at all. It uses the following example: show that f(x) = x^2 + 2x + 1 is O(x^2)

    My first question is, what value of x do i start with?? i dont know how one chooses a value of x to start with. in the book, it starts with x > 1. I dont understand how they came up with 1 instead of 2, 3 or any other number.

    if someone could please answer my question and also explain the big-o notation in an easy to understand way with an example, it would be great. thanks a lot in advance! i really appriciate it.
    f(x) \in O(g(x))

    means that for big enough \displaystyle x: |f(x)| is less than (or equal) some fixed multiple of \displaystyle g(x). This means that there exists an  x_0 such that for all  x\ge x_0, and a k>0:

    |f(x)|\le k g(x)

    In the case of your example for all  x \ge 1 ;  x^2\ge x and x^2 \ge 1. Hence for all x \ge 1

    |f(x)|=f(x)=x^2+2x+1\le x^2+2x^2+x^2=4x^2

    Hence f(x) \in O(x^2) (using x_0=1,\ k=4)

    CB
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