musiclink213

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So, i just had my calc test, and I'm not asking for homework help. but there was one question that i just couldn't get. it went something like this:

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.
 

honsano

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I don't know my calculus so I am gonna just say it is one. One over x is just zero because 1 over infinity and therefore you get 1 over 1....right? I dunno, hope it helps and someone with better calc. skills will come along soon enough to help you out and give you a sure answer.
 

JayMiranti

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That function you gave seems to not make any sense... the whole thing is raised to the infinite power, or to the power of X?

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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Cerberus

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well, looks like jay was probably right though that certainly is an strange function.
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
 

BubbleBobble

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I think the answer is 1/e.

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.
 

musiclink213

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woops, i posted it incorrectly. the function is actually limit as x--> infinite of (1/(1+(1/x))^x

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

Cerberus

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Originally posted by musiclink213
woops, i posted it incorrectly. the function is actually limit as x--> infinite of (1/(1+(1/x))^x

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.
 

JayMiranti

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Yup i agree it is def 1/e

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.
 

91Bravo

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

smuwillobrien

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Well, we've got some really talented people on here. Considering the other stuff that gets asked on this board (i.e. anything by doctorcynical) I don't see it being inappropriate to ask a calculus question.
 

musiclink213

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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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