Timeline for What is a better way to explain these claims about limit are not true in general?
Current License: CC BY-SA 3.0
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| Jun 18, 2020 at 8:32 | history | edited | CommunityBot |
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| Jul 4, 2016 at 8:53 | answer | added | Benoît Kloeckner | timeline score: 3 | |
| Jun 26, 2016 at 1:06 | comment | added | James S. Cook | It is important to group these examples as a common problem... the "indeterminant form". In this way, you get them to think of them as one difficult problem to understand (with 7 facets) verses 7 completely different weird places where arithmetic explodes. It's just semantics, but, I find the use of a universal term to point them to the similarity of (1) and (2) is helpful. Ambiguity with improper integrals likewise fall into one of the usual indeterminant forms (ignoring pathological examples which only mathematicians can understand or care about) | |
| Jun 25, 2016 at 8:47 | answer | added | leftaroundabout | timeline score: 2 | |
| Jun 24, 2016 at 20:03 | vote | accept | CommunityBot | moved from User.Id=2139 by developer User.Id=3 | |
| Jun 24, 2016 at 17:44 | answer | added | Henry Towsner | timeline score: 6 | |
| Jun 24, 2016 at 17:34 | answer | added | Daniel R. Collins | timeline score: 2 | |
| Jun 24, 2016 at 16:46 | answer | added | Daniel Hast | timeline score: 11 | |
| Jun 24, 2016 at 13:22 | answer | added | Math Misery | timeline score: 4 | |
| Jun 24, 2016 at 11:50 | comment | added | user797 | (3) is obviously correct... provided $f$ and $g$ are nonnegative! Sometimes, these errors have a kernel of truth to them. In such a scenario, I imagine it helps to more detail (e.g. to clearly define the conditions they have in mind, and to give them experience with what sorts of functions to go to for counterexamples) rather than just talk about the general case. | |
| Jun 24, 2016 at 10:42 | comment | added | Dan Fox | With respect to the first example, an example that shows the fallacy of the cancellation argument is something like $\lim_{x\to \infty}(x - \sqrt{x + 1})$. There results $\infty - \infty$, but the limit is infinite too. One way to help students gain intuition is to have them compute the limits approximately by plugging in values (e.g. using a computer). | |
| Jun 24, 2016 at 8:45 | history | edited | user2139 | CC BY-SA 3.0 |
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| Jun 24, 2016 at 8:26 | history | asked | user2139 | CC BY-SA 3.0 |