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baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
\[\lim_{x\to 0}\left(\frac{(1+x)^{\frac{1}{x}}}{e}\right)^{\frac{1}{x}}.\]
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
sorry, thats kind of hard to see.
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
\[\LARGE \lim_{x\to 0}\left(\frac{(1+x)^{\frac{1}{x}}}{e}\right)^{\frac{1}{x}}.\]
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.2
\[ \Large e = \lim_{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^n \]When you reparameterize: \(x=1/n\) \[\Large e = \lim_{x \rightarrow 0}\left(1+x\right)^\frac{1}{x} \]
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.2
So it's a matter of settling that outer 1/x
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
I haven't learned 'reparameterize' yet, so I would assume I wouldn't have to use that... Supposed to use L'Hospital's rule
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.2
Okay, then you need to have an indeterminate form of \(\infty /\infty\) or \(0/0\)
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1353045336700:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1353045499277:dw
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
@mahmit2012 I am supposed to use L'Hospital's rule.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.2
I can't read that bottom line.
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
"and in this case it is 1/sqrt(e)
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.2
No, of the previous picture
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
I don't know
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.2
Okay, let's start with bringing in the \(1/x\) to the numerator and denominator and figuring out if that is an indeterminate form.
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1353047217870:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1353047297672:dw
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
@waterineyes can you help me understand this maybe?
 2 years ago
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