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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: 92,237

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

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

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: 92,237

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

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

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: 92,237

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

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

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: 92,237

But doesn't it follow?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

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.

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: 92,237

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.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

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

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: 92,237

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

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

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

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: 92,237

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

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

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

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: 92,237

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

**In mathematics, you don't understand things. You just get used to them.**

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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: 6,732

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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