The proofs of [tex]y = \displaystyle\lim_{x \to\infty} (1 + 1/x)^{x} = e[/tex] that I have seen basically involve taking the natural log of both sides and getting the equation in a form where L'Hopital's rule can be applied. The problem I have with this is that it requires taking the derivative of the natural log function, and the proof of the derivative of(adsbygoogle = window.adsbygoogle || []).push({}); thatrequires prior knowledge that the limit above converges to e! It all seems a bit circular - is there a proof of the limit of the compound interest function that doesn't involve using L'Hopital's rule?

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# Proof of the value of e without using L'Hopital's rule?

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