(adsbygoogle = window.adsbygoogle || []).push({}); ANOTHER really basic question... this time regarding e :D

Hello,

As some of you well know, I'm reading through some lecture notes on single-variable calculus. The teacher who wrote these notes gives a proof of exp'(x)=exp(x). He wrote this inequality:

[((1+1/n)^n)-1]n ≤ [(e^h)-1]/h≤ [((1+1/n)^n+1)-1]n

Where h=1/n.

Now, I get why this inequality is true, but the teacher says that the right and left sides go to 1 as n--->∞. He said to use the binomial expansions to see this. I'm not getting it. Could someone help?

Thanks(again)

mathguy

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# ANOTHER really basic question this time regarding e

**Physics Forums | Science Articles, Homework Help, Discussion**