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#1 2013-01-07 08:45:52
- anonimnystefy
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A weird limit!
Hi
Can anyone help me with the following limit:
I know that it should be equal to 1/2 and the the Stolz theorem is supposed to be used, but I cannot get the final result...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#2 2013-01-07 09:12:31
- bobbym
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Re: A weird limit!
Hi;
Does this help?
http://topologicalmusings.wordpress.com … o-theorem/
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#3 2013-01-07 09:25:07
- anonimnystefy
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Re: A weird limit!
No. I already looked at that page. It just gets the limit to the indeterminate from 0*infinity...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#4 2013-01-07 09:51:59
- bobbym
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Re: A weird limit!
We need to use the binomial theorem here now.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#5 2013-01-07 09:54:32
- anonimnystefy
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Re: A weird limit!
Do you see the n/(p+1) part? It makes it not possible to use Stolz like that.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#6 2013-01-07 09:57:02
- bobbym
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Re: A weird limit!
We are not allowed to split that limit?
Probably not, the two pieces are both equal to infinity.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#7 2013-01-07 10:07:31
- anonimnystefy
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Re: A weird limit!
That is right.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#8 2013-01-07 10:14:58
- bobbym
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Re: A weird limit!
I am trying to put it into the required form but the algebra is hideous.
The above limit equals 1 / 2 . But the limit is very difficult to handle.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#9 2013-01-07 10:58:08
- anonimnystefy
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Re: A weird limit!
I already got that much. That limit there is the problem...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#10 2013-01-07 11:04:05
- bobbym
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Re: A weird limit!
You got that far! How the heck did you get there?
Maybe we can use Stolz again?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#11 2013-01-07 11:12:44
- anonimnystefy
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Re: A weird limit!
It wasn't hard.
I don't think ot would get much prettier...
Last edited by anonimnystefy (2013-01-07 11:13:11)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#12 2013-01-07 11:42:20
- bobbym
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Re: A weird limit!
Why do you think this is a job for Stoltz then?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#13 2013-01-07 11:51:08
- scientia
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Re: A weird limit!
bobbym wrote:
The above limit equals 1 / 2 . But the limit is very difficult to handle.
Consider the numerator (ignoring the minus sign outside the fraction). Notice that the terms in and vanish so the highest power of is . Its coefficient is . Now look at the denominator. The highest power of is also and its coefficient is . Hence the limit as is
using the following rule:
If
and and then
Last edited by scientia (2013-01-07 20:52:47)
#14 2013-01-07 12:17:22
- anonimnystefy
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Re: A weird limit!
Wow! That is amazing! Thank you! 
Last edited by anonimnystefy (2013-01-07 12:17:45)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#15 2013-01-07 20:48:04
- scientia
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Re: A weird limit!
You're welcome. 