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DLS
 one year ago
Best ResponseYou've already chosen the best response.2\[\LARGE \lim_{x \rightarrow 0} \frac{(1+x)^\frac{1}{x} e}{x}\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0Taylor Series expansion?

experimentX
 one year ago
Best ResponseYou've already chosen the best response.0Taylor series works

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0Weird. The Taylor Series expansion is in the terms of \(e\) and \(x\). The first term is \(e\)

experimentX
 one year ago
Best ResponseYou've already chosen the best response.0gives e/2 if you calculate correctly

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0Oh wait! lol, yeah. I forgot to consider that e/2 which had no \(x\)

DLS
 one year ago
Best ResponseYou've already chosen the best response.2How about a different way rather than taylor series?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0Definition of derivative? :

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0I was just thinking how this might be the definition of a derivative in disguise.

experimentX
 one year ago
Best ResponseYou've already chosen the best response.0Binomial expansion might work ... but that's too long

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0DLS Use whatever you want. 15 minutes ago DLS How about a different way rather than taylor series? 9 minutes ago

DLS
 one year ago
Best ResponseYou've already chosen the best response.2You are right,still investigating for more methods,I wrote so to specify that you are not bound to any particular method,just asking if you know anything alternate :)

experimentX
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=Limit%5B%281+%2B+x%29%5E%281%2Fx%29+%281%2F%28x+%281+%2B+x%29%29++Log%5B1+%2B+x%5D%2Fx%5E2%29%2C+x+%3E+0%5D after using L'hopital you get this expression. The first term tends to e .. if you again apply L'hopital on the second term, you will get 1/2
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