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jackAt the weekend, I watched Mean Girls. Near the end, there's a scene where the protagonist has to answer a bonus sudden-death question in an inter-school math quiz, lim x->0 of log(1-x)-sin(x) over 1-cos2(x).
I followed up by googling the limit she had to find, and lo, unsurprisingly, there were people discussing it. There's just something weird about that.
In fact, it was pretty well chosen. It was on the screen for only a second, and they could have put gibberish there, but it was correct, and something you *could* solve in your head if you were on the ball.
Of course, I'm way out of practice, which is rather depressing. I remember lots of things, but to use them I need to write it all out from scratch, there's nothing I can do confidently.
As it happens, I nearly got this right, but unsurprisingly messed up the taylor expansions. I thought they'd used "has no limit" for "limit of infinity", but no, it's right, the sign is different above and below, so there is definitely no limit.
But then it occurred to me that that was probably contentious in itself. If f(x)->oo, devoid of context, I'd say nothing but "limit of infinity". But someone would say, it has no limit. After all, there's no actual number in the domain which is the limit. But in all applications I'm familiar with, knowing that tends to inf is useful.
Would anyone go with the "no limit" answer?
I followed up by googling the limit she had to find, and lo, unsurprisingly, there were people discussing it. There's just something weird about that.
In fact, it was pretty well chosen. It was on the screen for only a second, and they could have put gibberish there, but it was correct, and something you *could* solve in your head if you were on the ball.
Of course, I'm way out of practice, which is rather depressing. I remember lots of things, but to use them I need to write it all out from scratch, there's nothing I can do confidently.
As it happens, I nearly got this right, but unsurprisingly messed up the taylor expansions. I thought they'd used "has no limit" for "limit of infinity", but no, it's right, the sign is different above and below, so there is definitely no limit.
But then it occurred to me that that was probably contentious in itself. If f(x)->oo, devoid of context, I'd say nothing but "limit of infinity". But someone would say, it has no limit. After all, there's no actual number in the domain which is the limit. But in all applications I'm familiar with, knowing that tends to inf is useful.
Would anyone go with the "no limit" answer?
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Date: 2007-06-05 03:37 pm (UTC)I would say that "limit of infinity" is a subcase of "no limit": you're stating that there's no finite limit and you're giving additional information about the function's behaviour on top of that. So both are accurate, the former is preferable because it provides more information, and only a total pedant (and not in a good way) would insist on the latter.
no subject
Date: 2007-06-05 03:56 pm (UTC)Hmmm. I don't know. Obviously it isn't an *ideal* question. But then what is? You can only test real maths so much, applying techniques is useful, and applicable to a first-buzzer system. If you're looking to test L'Hopital, or something specific, then you could concentrate on that, but being able to simplify efficiently seems like a useful skill -- many real problems, end up in a state like that, needing a series of simplifications to boil down to a single answer.
That of course ignores the fact I *totally* forgot to look for trivial trigonometric simplifications before I started. Ahem.
I would say that "limit of infinity" is a subcase of "no limit":
Ah, yes, thank you, that says it perfectly. It sounds odd because limit is being used in slightly different ways, but it's the right answer afaict.