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I was reading on the big O/little O notation etc. and I understand the definitions, but how exactly would I use it to find the order of an expression/function?

I am asked to determine the order of $\sqrt{\epsilon(1-\epsilon)}$ and $4\pi^2\epsilon$ as $\epsilon \rightarrow 0$. But how would I do that?

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    You should divide by the $\epsilon^p$ and see for which $p$ the expression goes to zero as $\epsilon$ goes to zero. Then choose an $\epsilon$ near the supremo of such p's.2012-02-20
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    Thanks @chessmath. May I ask -- where does the $\epsilon ^p$ come from?2012-02-20
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    The main idea is that $\epsilon^p$ is an infinitesimal of order $p$ and an infinitesimal of "larger" order goes to zero "fast".2012-02-20

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