What Does Leading Correction Mean in Mathematical Contexts?

[1saac]

Homework Statement

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.

 

[rude man]

"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.