Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #201 2011-07-30 00:04:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Limits!

Hi;

Then you must know that the answer is pi^2 / 6.

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.

Offline

## #202 2011-07-30 00:07:27

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

Yes, I was tring to prove that without using series.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #203 2011-07-30 00:13:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Limits!

I get it now!

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.

Offline

## #204 2011-08-02 06:09:06

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

17)

Last edited by gAr (2011-08-02 06:14:13)

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #205 2011-08-02 10:22:01

Member
Registered: 2011-05-11
Posts: 171

### Re: Limits!

gAr & my edit wrote:

16)

The limit needs to approach from the right side of 0,
as amended above.  There aren't any real values for
ln(x) from the left side of 0, so it is undefined there.

Signature line:

I wish a had a more interesting signature line.

Offline

## #206 2011-08-02 16:10:03

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #207 2011-08-02 17:31:53

Member
Registered: 2011-05-11
Posts: 171

### Re: Limits!

gAr wrote:

I am not "forgetting about" ln(1 - x). I was looking right at it and working with it, regardless if I mishandled it. x approaching 0 from either side is not an issue for ln(1 - x), as it is 0. But x approaching 0 from the left side of ln(x) is a problem, just as it is for x approaching from the left of, say, x^x, as those limits do not exist. And where is ln(-x) = ln(x) + ipi coming from? And then, why isn't your alleged expression this

instead of what you typed, because you assumed x --->0-? ----------------------------------------------------------
-------------------------------------------
And
----------------------------------------------------- on using

Last edited by reconsideryouranswer (2011-08-02 17:56:25)

Signature line:

I wish a had a more interesting signature line.

Offline

## #208 2011-08-02 17:43:10

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #209 2011-08-02 20:10:57

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

Anyway,

Have you read about complex numbers? It exists and it is -∞

and this is 1

Last edited by gAr (2011-08-02 20:14:25)

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #210 2011-08-03 02:38:07

Member
Registered: 2011-05-11
Posts: 171

### Re: Limits!

gAr wrote:

and this is 1

Look at all of those negative x-values approaching 0 from the left where x^x is real.

For example, x =

-1/5, -1/25, -1/125, -1/625. -1/3125, ...

For these, x^x is approaching -1.

Signature line:

I wish a had a more interesting signature line.

Offline

## #211 2011-08-03 02:51:14

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

I would suggest you to go to www.wolframalpha.com
and enter this:

``Limit[x^x,{x->0},Direction->1]``

That would show you a graph along with the answer.
If you observe the graph, you'll see that the complex part approaches 0, and the real part approaches 1.

How did you calculate that it would approach -1? They should have been complex numbers, with positive real part.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #212 2011-08-03 06:57:29

Member
Registered: 2011-05-11
Posts: 171

### Re: Limits!

gAr wrote:

How did you calculate that it would approach -1?
They should have been complex numbers, with positive real part.

Notice in the folowing lines how I will use fractions that
necessarily have odd denominators (for odd indices)
Let me show three of my examples worked out:

-------------------------------------------------------------

-------------------------------------------------------------

-------------------------------------------------------------

I will use a fraction relatively much closer to 0:

-------------------------------------------------------------

Signature line:

I wish a had a more interesting signature line.

Offline

## #213 2011-08-03 13:40:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Limits!

Hi;

That is not correct.

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.

Offline

## #214 2011-08-03 16:15:02

Member
Registered: 2011-05-11
Posts: 171

### Re: Limits!

bobbym wrote:

Hi;

That is not correct.

No, the odd root of a negative integer is some type of negative real number.
It must be.

Signature line:

I wish a had a more interesting signature line.

Offline

## #215 2011-08-03 16:34:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Limits!

No, the odd root of a negative integer is some type of negative real number.
It must be.

Yes but check this out! You are forgetting there are also complex answers.

This is one answer for (-1)^(1/3)

Are not the roots of

,
,

What I am saying is just because (-1)^3 = -1 that does not mean ( -1) ^(1 / 3 ) is -1 solely. There are other answers. 3 of them as a matter of fact.

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.

Offline

## #216 2011-08-03 18:54:52

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #217 2011-08-04 03:57:48

Member
Registered: 2011-05-11
Posts: 171

### Re: Limits!

bobbym wrote:

Yes but check this out! You are forgetting there are also complex answers.

This is one answer for (-1)^(1/3)

Are not the roots of

,
,

Signature line:

I wish a had a more interesting signature line.

Offline

## #218 2011-08-04 04:08:04

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Limits!

sqrt(-1) doesnt exist because it is indefined.

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.

Offline

## #219 2011-08-04 04:47:35

Member
Registered: 2011-05-11
Posts: 171

### Re: Limits!

anonimnystefy wrote:

sqrt(-1) doesnt exist because it is indefined.

----------------------------------------------------------------------------------------------

*** Edit***  I will stop posting to this subject thread for the foreseeable future.

Last edited by reconsideryouranswer (2011-08-04 06:12:39)

Signature line:

I wish a had a more interesting signature line.

Offline

## #220 2011-08-04 05:36:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Limits!

Hi;

You are making heavy use of the principal value of a square root being only the positive answer. But does that apply for cube roots and higher?

http://mathworld.wolfram.com/CubeRoot.html

Both Mathematica and Maple do not agree.

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.

Offline

## #221 2011-08-04 22:10:28

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

18)

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #222 2011-08-04 22:12:12

bob bundy
Registered: 2010-06-20
Posts: 8,337

### Re: Limits!

hi guys,

Sorry to jump in on your thread but would you mind casting an eye over

http://www.mathisfunforum.com/viewtopic … 03#p184503

Thanks,

Bob

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

Offline

## #223 2011-08-04 22:18:19

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### Re: Limits!

Hi Bob,

I was also confused with that, so couldn't reply!
Anyway, I'll try again.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

## #224 2011-08-04 22:27:44

bob bundy
Registered: 2010-06-20
Posts: 8,337

### Re: Limits!

hi gAr

Thanks for the response.

I'm happy with the substitution leading to the final DE.  I'm really rusty on second order DEs having last done them about 30 years ago, so I was hoping for a second opinion on my final post.

Thanks

ps.  I'm being called into the garden to help my wife so I'll log back in later.

Bob

Last edited by bob bundy (2011-08-04 22:28:35)

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

Offline

## #225 2011-08-05 00:22:13

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Limits!

hi gAr

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.

Offline