Thursday, 1 August 2019

Can all limits be solved without L'Hopital?




Is there any type of limit that requires L'Hopital's rule to solve or can all limits be solved without using it?



If all limits can be solved without L'hopitals, is there some sort of proof or intuition for this?


Answer



Usually Taylor's expansion has the same strength. However, if you prohibit both L'Hopital and Taylor, then I doubt that limx0sinxxx3 or limx0sinxx+x3/6x5 can be solved elementary, without using the ideas of L'hopital or Taylor in some sense.


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