Reminds me of a discussion with a friend (who is not a mathematician) about how to solve limits like sin(3x^2)/(1-cos(x)) as x->0. He said that they were taught to use L'Hôpital and nothing can be as simple; I said 6. (asymptotic expansions ftw)
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Replying to @lisyarus @InertialObservr
Fwiw: both methods are effectively the same
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Replying to @Quasilocal @InertialObservr
Well, not really. L'Hôpital would make you to compute the derivative first, which for the aforementioned expression is quite messy. With asymptotics you just rewrite as 3x^2/(x^2/2) and you are done.
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Of course, the underlying theory is the same, if this is what you mean.
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I am sure you meant Taylor expansions. Asymptotics are an entirely different kind of beast ;)
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Well, I've always heard the term "asymptotic expansion near a point" to mean exactly Taylor series.
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interesting i've only ever heard asymptotic expansion to be an expansion about z=infinity
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Yep, that's why I added "near a point".
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Fair.. Though this conversation is also rather pointless since we all clearly know how to do whatever the hell we're calling by different names
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"near a point" & "pointless" I see what you did there
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i only wish i could say that was on purpose
10:22 AM - 18 Jul 2019
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