They both get closer to but never reaching zero. Is the reason simply that one gets 1/x^2 gets closer to zero faster? So whats the threshold for something to be considered finite or infinite?
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Yes, the reason is that one approaches zero fast enough and the other doesn’t. There is a threshold in the sense that if you consider 1/x^a then it has finite area for a>1 and infinite otherwise. On the other hand they are not considered finite or infinite, they are actually and factually finite or infinite. Also, anything that approaches zero faster than 1/x^2 has finite area under the curves, but the converse is not generally true. You can even have functions with finite area that don’t approach 0 at all (at least on some points).
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