Quantcast

i know my calculus

This forum made possible through the generous support of SDN members, donors, and sponsors. Thank you.

musiclink213

My room is a mess
7+ Year Member
15+ Year Member
Joined
Oct 20, 2003
Messages
3,479
Reaction score
3

Members don't see this ad.
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

Senior Member
10+ Year Member
15+ Year Member
Joined
Feb 8, 2001
Messages
215
Reaction score
12
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

Senior Member
7+ Year Member
15+ Year Member
Joined
Oct 17, 2003
Messages
147
Reaction score
0
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
 

getcloned

Hilton Magician
10+ Year Member
15+ Year Member
Joined
Feb 23, 2004
Messages
79
Reaction score
0
isnt that the same as saying (1/1)^inf?

so it would be 1.

it's been a few years though!
 

Cerberus

Heroic Necromancer
15+ Year Member
Joined
Dec 13, 2001
Messages
15,128
Reaction score
186
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

Where's the "any" key?
7+ Year Member
15+ Year Member
Joined
Nov 23, 2003
Messages
394
Reaction score
2
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

My room is a mess
7+ Year Member
15+ Year Member
Joined
Oct 20, 2003
Messages
3,479
Reaction score
3
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.
 

SilleAngyl

Member
7+ Year Member
15+ Year Member
Joined
Oct 21, 2003
Messages
88
Reaction score
1
The answer is: you + me = us
Duh!
 

Cerberus

Heroic Necromancer
15+ Year Member
Joined
Dec 13, 2001
Messages
15,128
Reaction score
186
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

Senior Member
7+ Year Member
15+ Year Member
Joined
Oct 17, 2003
Messages
147
Reaction score
0
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.
 

Bad Mojo

Cold as Ice
7+ Year Member
15+ Year Member
Joined
Jul 12, 2003
Messages
293
Reaction score
2
Oh yea, its infinity + 1!!!!!
 

91Bravo

Frank Netter's Love Child
7+ Year Member
15+ Year Member
Joined
Oct 17, 2002
Messages
140
Reaction score
0
Seriously.....since when did this place become an online tutoring service?!
 

smuwillobrien

Senior Member
15+ Year Member
Joined
Sep 6, 2003
Messages
846
Reaction score
3
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.
 

Cerberus

Heroic Necromancer
15+ Year Member
Joined
Dec 13, 2001
Messages
15,128
Reaction score
186
well, I am a math major and really enjoy the lower level calculus stuff. It reminds me of simpler times, times without proofs :D
 

musiclink213

My room is a mess
7+ Year Member
15+ Year Member
Joined
Oct 20, 2003
Messages
3,479
Reaction score
3
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,.
 
Top