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Mathematics 101 Online
OpenStudy (anonymous):

I am trying to show that for every \(\epsilon>0\), there exists an \(N\in\mathbb{N}\) such that\[\left|\left(\frac{x}{n}+1\right)^n-e^x\right|<\epsilon\]whenever \(n\geq N\). How can I go about doing this? This a problem about uniform convergence.

OpenStudy (anonymous):

By the way, \(n\in\mathbb{N}\) and \(x\in[-A,A]\).

OpenStudy (anonymous):

@satellite73 @Zarkon @JamesJ @Vernard_Mercader_PhD @brinethery

OpenStudy (jamesj):

The careful proof of this is not achieved in a couple of lines. One book that works through this carefully is Spivak's "Calculus" Spivak is my favorite introduction to analysis and I recommend you pick up a copy, even if it's from your library.

OpenStudy (anonymous):

I'm so stuuuupid! That was from 6 years ago, I can't even remember what I had for breakfast lol.

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