Math Is Fun Forum

princess snowwhite

Member

Registered: 2012-11-06

Posts: 29

finding limit

((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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: finding limit

The first limit is 1 for every c.

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“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: finding limit

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: finding limit

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

But doesn't it follow?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: finding limit

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.
“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: finding limit

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.
“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: finding limit

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.
“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: finding limit

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.
“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding limit

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathteacher005

Member

Registered: 2012-11-12

Posts: 1

Re: finding limit

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!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: finding limit

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob