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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,827

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

No. I already looked at that page. It just gets the limit to the indeterminate from 0*infinity...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,827

We need to use the binomial theorem here now.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Do you see the n/(p+1) part? It makes it not possible to use Stolz like that.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,827

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

That is right.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,827

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.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

I already got that much. That limit there is the problem...

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,827

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.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

It wasn't hard.

I don't think ot would get much prettier...

*Last edited by anonimnystefy (2013-01-06 12:13:11)*

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,827

Why do you think this is a job for Stoltz then?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

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 (2013-01-06 21:52:47)*

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Wow! That is amazing! Thank you!

*Last edited by anonimnystefy (2013-01-06 13:17:45)*

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

You're welcome.

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