What Does Leading Correction Mean in Mathematical Contexts?

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Homework Statement



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Homework Equations



What is a leading correction?

The Attempt at a Solution



I easily proved the limits, however I do not know what a "leading correction" is. I googled it and I can't seem to find a precise definition.
 
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"Leading" is apparently used by the Brits and their colonies [OK, FORMER colonies :-) ] for "first-order" .

Like, sin x = x - x^3/3! is the leading correction to sin x = x.
 
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