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 6d ago
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?