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Taken literally, the centre of mass formulae for a 2d shape will give you the centre of a lamina that's described by two given functions between 2 limits. But I wondered if they might also represent something else more abstract with certain types of functions.

Can the centre of mass formulae be interpreted in any other way?

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I was about half-way through answering your L'Hospital's Rule question (for the simplest version of the rule). Constructive criticism of the way you pose the question should not be taken as an indication that you need to delete the question, it should be an indication that you need to put a bit more thought and effort into it. –  Arturo Magidin Feb 19 '12 at 23:02
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A center of mass is just an average. You can have all kinds of averages. For example, you can find the average location of the population of the United States, which has been slowly moving westward for the last couple of hundred years.

Mathematically, there are various generalizations. You can have a density that's not constant. You can have 1 or 3 dimensions, or any other number.

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