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anonymous
 5 years ago
lim (1  1/x)^(x) as x>+infinty
anonymous
 5 years ago
lim (1  1/x)^(x) as x>+infinty

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you please explain to me how you got that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you let x = infinity. Then what is 1/x really equal to?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0My solution? Please correct me then sir.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think this is a special identity representing e, but let me check.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If my Cal I recall is correct, if the exponent was positive, it is the wellrecognized lim that goes to e. The fact that exponent is is negative, I am leaning to agree with you it goes to 0. How did you reach your conclusion.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, You have something that is always smaller than one being raised to big negative numbers. It will certainly not tend toward 0 because the exponentiation will grow faster than the 1/x will shrink. However I think it does converge on e rather than go on to infinity.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's 11, how do you get 1? And it's to the x, meaning the equation is actually 1/(11/x) which is certainly zero.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No. It is \[(1\frac{1}{x})^{x}\] I agree that the fraction will tend toward 0, but the whole expression tends toward \(1^\infty\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually I contend that inside the bracket goes to 1 because \[(1 \div \infty)\] tends to zero.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh my bad didn't see 11/x, even then the resultant inside is still zero. 0^infinity = 0.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it's not \(1\infty\) it is 1 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0God I need to stop failing and go to bed lol. I'm sorry polpak you're right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But that is leaves us with \(\frac{1}{1^\infty}\) which is undetermined form and needs special handling with l'hopital.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Have to take the log to bring down the x out of the exponent, then take the derivative, etc. It's kind of a bear. It looks like it might be e though.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We need Lokisan for this one. We need someone who has read everything concerning the number or the limit e.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Heh. Well I checked with Alpha, and it's definitely e. Glad I don't have to do this for my homework though.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=lim+as+x+goes+to+infinity+%281++1%2Fx%29^%28x%29
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