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find the limit as x--> infinite of (1/(1+(1/x))^infinite. anybody know how to solve it? i ended up with my final answer as e, but I'm not sure if that's right.

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- Thread starter musiclink213
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find the limit as x--> infinite of (1/(1+(1/x))^infinite. anybody know how to solve it? i ended up with my final answer as e, but I'm not sure if that's right.

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If it is correct as written, it seems like the answer is 1.

as x gets large, 1/x approaches 0, so the function gets closer and closer to (1/(1+0))^inf

which is the same as 1^inf (since 1/(1+0) is 1)

and 1 to any power is equal to one..

howd u come up with E?

if i have lead you astray ill be glad to help

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take this:

Lim x->infinity (1/(1+(1/x))^y

since 1/x approaches zero as x approaches infinity we have

(1/(1+0))^y=(1/1)^y=(1)^y=1

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Here is my reasoning:

lim x->inf (1/(1+(1/x)))^inf = lim x->inf (1^inf)/(1+(1/x))^inf

The numerator is clearly 1.

Since the definition of e = lim x->inf (1 + 1/x)^x, the denominator is equal to e.

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sorry, i was very upset and didn't realize what i was typing.

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The answer is: you + me = us

Duh!

Duh!

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Originally posted by musiclink213

sorry, i was very upset and didn't realize what i was typing.

in that case the answer is e^-1 from the reasons bubble gave.

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it helps to know your definitions

the method i said earlier is wrong because it doesnt take into account that the denomenator must be larger than one, since it is (1. something) that is being multiplied over and over, thus increasing the value each time, giving e.

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Originally posted by 91Bravo

Seriously.....since when did this place become an online tutoring service?!

actually, i posted after the test, about a specific problem. did i ask for someone to explain all of calc 2 to me? no. i see no problem with asking a question or two that could majorly help someone, especially when you have a calc prof. like mine, who doesn't teach and only complains about his arm,.

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A