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DLS
 3 years ago
Limits question [Challenge]
DLS
 3 years ago
Limits question [Challenge]

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

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

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

ParthKohli
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0gives e/2 if you calculate correctly

ParthKohli
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.2How about a different way rather than taylor series?

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

ParthKohli
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0Binomial expansion might work ... but that's too long

ParthKohli
 3 years 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
 3 years 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
 3 years 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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