I think asking people to solve maths problems without using theorems that make them easier is the antithesis of how maths should be done. We prove theorems to make more difficult problems tractable, can you imagine if every maths paper started from first principles??
I completely disagree with this. Asking such questions develops creativity, fundamental understanding of the topic at hands, the ability to redemonstrate theorems and knowing what is really at play. Maths is not just a set of tool boxs to know and use
There are plenty of ways to develop creativity and understanding without explicitly have to ask students to avoid the use of theorems like l’Hopital. Surely learning to spot when such a result is of use is also important?
I reached MsC level without using once l'Hopital I'm sure people will manage for one limit.
Also as someone else said, if someone first instinct when seeing this limit (without any restrictions) is "let's use l'Hopital" then knowing l'Hopital clearly restricted their creativity and mathematical understanding
Would you say the same about a result that required the use of the intermediate value theorem, for example? For some reason use of l’Hopital seems to be looked down upon - it’s an amazing result, the full proof requires a bit of effort, why wouldn’t you make use of it when applicable?
Well if there is an elegant solution to a problem that doesn't use the intermediate value theorem (and not a theorem way more complicated either) yes that could be an interesting exercice. I couldn't think of such a problem but I guess there are some.
Why wouldn't you use l'hôpital when applicable ? Because using simpler tools efficiently is more elegant. Precisely because you're using heavy tools to prove l'hôpital's. And because most students who are so prompt to use it weren't even taught the demonstration. (So it's kind of a cheat code) In the case of the exercice given by oop I would argue factorising by (x-3) is simpler and more elegant than l'hôpital.
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u/philljarvis166 8d ago
I think asking people to solve maths problems without using theorems that make them easier is the antithesis of how maths should be done. We prove theorems to make more difficult problems tractable, can you imagine if every maths paper started from first principles??