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

Login

Username

Password

Not registered yet?

#201 2011-07-30 22:04:30

bobbym
Administrator

Offline

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#202 2011-07-30 22:07:27

gAr
Star Member

Offline

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."
 

#203 2011-07-30 22:13:02

bobbym
Administrator

Offline

Re: Limits!

I get it now!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#204 2011-08-03 04:09:06

gAr
Star Member

Offline

Re: Limits!

17)


Last edited by gAr (2011-08-03 04:14:13)


"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."
 

#205 2011-08-03 08:22:01

reconsideryouranswer
Full Member

Offline

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.
 

#206 2011-08-03 14:10:03

gAr
Star Member

Offline

Re: Limits!


                         roll


"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."
 

#207 2011-08-03 15:31:53

reconsideryouranswer
Full Member

Offline

Re: Limits!

gAr wrote:

roll

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
----------------------------------------------------- shame on using roll

Last edited by reconsideryouranswer (2011-08-03 15:56:25)


Signature line:

I wish a had a more interesting signature line.
 

#208 2011-08-03 15:43:10

gAr
Star Member

Offline

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."
 

#209 2011-08-03 18:10:57

gAr
Star Member

Offline

Re: Limits!

I see that you edited your post instead of replying.
Anyway,

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

and this is 1

Last edited by gAr (2011-08-03 18:14:25)


"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."
 

#210 2011-08-04 00:38:07

reconsideryouranswer
Full Member

Offline

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.
 

#211 2011-08-04 00:51:14

gAr
Star Member

Offline

Re: Limits!

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

Code:

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."
 

#212 2011-08-04 04:57:29

reconsideryouranswer
Full Member

Offline

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.
 

#213 2011-08-04 11:40:31

bobbym
Administrator

Offline

Re: Limits!

Hi;

That is not correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#214 2011-08-04 14:15:02

reconsideryouranswer
Full Member

Offline

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.
 

#215 2011-08-04 14:34:57

bobbym
Administrator

Offline

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#216 2011-08-04 16:54:52

gAr
Star Member

Offline

Re: Limits!

reconsideryouranswer, do you admit that you do not know complex numbers?


"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."
 

#217 2011-08-05 01:57:48

reconsideryouranswer
Full Member

Offline

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.
 

#218 2011-08-05 02:08:04

anonimnystefy
Real Member

Offline

Re: Limits!

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#219 2011-08-05 02:47:35

reconsideryouranswer
Full Member

Offline

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 (2011-08-05 04:12:39)


Signature line:

I wish a had a more interesting signature line.
 

#220 2011-08-05 03:36:05

bobbym
Administrator

Offline

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#221 2011-08-05 20:10:28

gAr
Star Member

Offline

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."
 

#222 2011-08-05 20:12:12

bob bundy
Moderator

Offline

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,  smile

Bob


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

#223 2011-08-05 20:18:19

gAr
Star Member

Offline

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."
 

#224 2011-08-05 20:27:44

bob bundy
Moderator

Offline

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.  wave

Bob

Last edited by bob bundy (2011-08-05 20:28:35)


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

#225 2011-08-05 22:22:13

anonimnystefy
Real Member

Offline

Re: Limits!

hi gAr


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

Board footer

Powered by FluxBB