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- Next up, figure out which terms to "eliminate" to get an expression for x as q gets very large or small (but not taking an actual limit!?)
That's, essentially, big O/small o notation. It's extremely useful for visualising behaviours of all sorts of things, though, for some reason, it's mostly talked explicitly about by CS people. For example, f(x) = x + exp(-x) could be considered as two cases, one for x ≥ 0 (where exp(-x) contributes increasingly less the larger the x) and x < 0 (where behaviour is dominated by exp(-x)). Additionally, it means that regardless of what non-zero constants multiply those expressions (be mindful of the sign), big picture, the behaviour won't change.
And, yes, despite looking like handwaving difficulties away, it's actually a formal way of simplifying, discussing and solving problems.