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Big O Notation is an informal name of the "O(x)" notation used to describe asymptotic behaviour of functions. It is a special case of Landau notation, where the O is the Greek letter capital omicron. Please consider using the [landau-notation] tag instead if your question is related to small omicron, omega, or theta in Landau notation.

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Big O Proof , f(n) = 2n + 1 and I have to prove f(n) is O n^2

If I have $f(n) = 2n + 1$ and I have to prove $f(n) \in O(n^2)$, by proving there exists positive constants $c$ and $n_0$ such that $f(n)<cn^2, \forall n\ge n_0$, can I do this all in one step by put …
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How to prove Big-O when $f(n)$ is defined sectionwise

I'm given a function which is defined based on a condition, for example $$ f(n) = \begin{cases} 4n+1, \ \text{n is even}\\ 3n^2+2, \ \text{n is odd} \end{cases}. $$ I have to prove or di …
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