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#101 2011-06-29 22:41:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Limits!

Hi;

I got - ∞ for the one with the z in there. Thanks much for providing your solution.


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.

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#102 2011-06-29 22:48:25

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi,

Okay.
You could've figured it out that there could be a mistake.
Thanks for telling!


"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."

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#103 2011-06-30 00:48:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: Limits!

hi gAr

could you explain how you got the second line in your solution.i don't get it.


“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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#104 2011-06-30 01:01:08

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi anonimnystefy,

I used L'Hospital's rule.


"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."

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#105 2011-06-30 01:04:03

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: Limits!

aah.ok think i get it.

could you also make a topic on integrals?it would be nice to practice working on them.

Last edited by anonimnystefy (2011-06-30 01:05:20)


“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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#106 2011-06-30 01:12:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Limits!

Hi;

You can find a lot of them here.

http://www.mathisfunforum.com/viewtopic.php?id=4208


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.

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#107 2011-06-30 01:21:29

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi bobbym,

I was searching for that url. Thanks!


"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."

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#108 2011-06-30 01:25:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Limits!

Hi gAr;

I can not come up with anything better for #9 then using L'Hospitals rule.


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.

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#109 2011-06-30 01:45:27

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Okay, no problem.
Thanks for looking into the problem.


"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."

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#110 2011-06-30 01:48:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Limits!

Hi;


This works. Taylorize the numerator:

Now divide through by x and now it is easy to see what the limit is.


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.

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#111 2011-06-30 01:56:26

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi bobbym,

Yes, I tried expanding like that.
But deriving that would require us to find limits anyway!


"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."

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#112 2011-06-30 01:59:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Limits!

Hi;

Do you mean the derivatives, because the limits are done term by term?

Yes, you would have to find and prove the general term of that series ( done by induction ). Once you have the general term it is easy to see all terms after the constant term have an x in them and therefore zero out.

Oh wait, I see what you are saying! Good point. Even the f(0) could be a problem.


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.

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#113 2011-06-30 02:10:25

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi,

Yes!
That's why I avoided giving that in my solution.

I thought maybe we can use binomial theorem, but that too fails. (or is it me?)


"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."

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#114 2011-06-30 02:13:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Limits!

Hi gAr;

That is one way, maybe.

Also this is like a piece of experimental math. You use a package to get the answer and then you prove the answer is correct by induction. Sort of like the more classical use of guessing at the solution of a sum or a recurrence.


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.

Offline

#115 2011-06-30 02:20:46

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi bobbym,

Yes, I agree.


"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

#116 2011-06-30 02:32:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Limits!

Hi;

In this case since proving the answer you get is going to be difficult at least from what I see, I think it is easier to use your way.


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.

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#117 2011-06-30 02:40:56

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi bobbym,

I think so. From what I know, no other tricks I can think of.


"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."

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#118 2011-07-01 04:43:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: Limits!

hi gAr

how about a hint on the 10?


“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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#119 2011-07-01 04:52:07

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi anonimnystefy,

It's already solved in #94.


"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."

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#120 2011-07-01 05:13:10

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Re: Limits!

I hope my steps are correct.

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#121 2011-07-01 05:19:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: Limits!

hi 123ronnie123

how did you get the next to last line?


“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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#122 2011-07-01 05:23:14

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Re: Limits!

Hi anonimnystefy,
I am unsure about the ending of my solution and I am waiting for either gAr's or Bobbym's help.

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#123 2011-07-01 05:43:54

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi 123ronnie321,


"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."

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#124 2011-07-01 06:12:25

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Re: Limits!

Thanks for your help, gAr. smile

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#125 2011-07-01 15:01:09

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Limits!

Hi,

You're welcome!


"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."

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