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**princess snowwhite****Member**- Registered: 2012-11-06
- Posts: 29

((1+cx)/(1-cx))^(1/x) tends to 4 as x tends to infinity.

find the limit of ((1+2cx)/(1-2cx))^(1/x) as x tends to infinity.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

Hi princess snowwhite;

For the first part of the question:

((1+cx)/(1-cx))^(1/x) tends to 4 as x tends to infinity.

I can not find any c that will give 4 as x approaches infinity.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

The first limit is 1 for every c.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

Hi;

That is what I am getting, so the question does not make any sense.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Maybe it is a misprint or a typo.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

Yes, it should read 1 instead of 4.

find the limit of ((1+2cx)/(1-2cx))^(1/x) as x tends to infinity

So the answer should be 1 because 2c=c.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

I don't think that is the misprint.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

But doesn't it follow?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Not really. The question would be close to trivial. I think the question is more likely to be asking for the constant c for which a limit has the value 4 and then finding the same limit but with 2c instead of the c, whose value we now know.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

anonimnystefy wrote:

The first limit is 1 for every c.

There is no c that will give a limit of 4. You said so yourself. The limit is independent of c. That is why it is trivial.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Yes. So I am thinking that it might be a typo of the function whose limit is being taken.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

Maybe the questioner just wants the OP to see that the answer is 1. To spot the inconsistency.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

This looks too much like a book problem. I do not think that is what it wants.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

Isn't the simplest typo that she wrote 4 when she meant 1?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Being simplest doesn't makng true. And, yes, I am familiar with the Occam's razor.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,193

I use Schick's or Gillette's razor for a better shave.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**mathteacher005****Member**- Registered: 2012-11-12
- Posts: 1

Hello! The answer is \lim_{x\to\infty }\left({{2\,{\it cx}+1}\over{1-2\,{\it cx}}}\right)^{{{1}\over{x}}} = 1.

You can check it here.

numberempire.com/limitcalculator.php?function=%28%281%2B2%2Acx%29%2F%281-2%2Acx%29%29%5E%281%2Fx%29&var=x&val=inf&answers=&limit_type=two-sided

My friend show me few weeks ago and now my students always use it for checking the answers:) Good Luck!

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,421

hi mathteacher005

Welcome to the forum and thanks for the link.

I will convert your post so that the expression is in Latex and the link easier to use.

numberempire.com/limitcalculator.php?fu … =two-sided

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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