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- Thread starter Swapnil
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arildno

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In asymptotic analysis.

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CRGreathouse

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[tex]\sin(x)=x-\frac{x^3}{6}+O(x^5)[/tex]

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arildno

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And isn't that, really, an expression for sin(x)'s asymptotic behaviour as x ambles peacefully off towards the origin?

(If you write sin(x) with an explicit remainder term, say, by utilization of the mean-value theorem for integrals, then it is of course something different, but we wouldn't use O's in that case).

(If you write sin(x) with an explicit remainder term, say, by utilization of the mean-value theorem for integrals, then it is of course something different, but we wouldn't use O's in that case).

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CRGreathouse

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arildno said:And isn't that, really, an expression for sin(x)'s asymptotic behaviour as x ambles peacefully off towards the origin?

Oh yes absolutely. It's just a different way of thinking about it.

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