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#176 2011-07-27 21:17:48

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

Re: Limits!

Hi bobbym,

Okay.
It simplifies finding some integrals.
You can add one more tool to your kit!


"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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#177 2011-07-28 01:12:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi gAr;

It looks like I can do them somewhat but I am having trouble understanding how differentiating produces an integral. I will look at more problems.


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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#178 2011-07-28 01:22:40

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

Re: Limits!

Hi,

Did you see this before? Good examples to evaluate some famous integrals:
http://www.math.uconn.edu/~kconrad/blur … derint.pdf


"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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#179 2011-07-28 01:34:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi gAr;

I have already downloaded it but have not looked at it. Thought I could get a feel for it with what I had. I will open it now.


Hey, that is a pretty good PDF.


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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#180 2011-07-28 03:19:06

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

Re: Limits!

I guess it's a long time!


"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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#181 2011-07-28 03:23:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi gAr;

I got most of his examples down.

Where did you use diff under the integral sign?


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

#182 2011-07-28 03:27:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,809

Re: Limits!

there is one very interesting limit:

Last edited by anonimnystefy (2011-07-28 03:27:41)


“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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#183 2011-07-28 03:27:53

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

Re: Limits!

Hi bobbym,

I used it on applying L'Hospital's rule, like in the example here


"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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#184 2011-07-28 03:33:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi gAr;

Okay, I will look at that too. Thanks for directing me to that PDF. I am not good at it yet but I can do some of them. That is a big improvement.

I also enjoyed the problem, even solving it the longer way. Thanks for posting it.


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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#185 2011-07-28 03:37:13

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

Re: Limits!

Hi,

I'm not good either.
I can do only the simple ones.

I'll take a short break, see you later.


"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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#186 2011-07-28 03:42:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Okay gAr, see you then.


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

#187 2011-07-28 05:06:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

gAr, have you noticed that using differentiation under the integral that the resulting integrands are much easier for the package to do?


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

#188 2011-07-28 05:13:17

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

Re: Limits!

Yes, they are!
Isn't it a wondderful tool?


"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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#189 2011-07-28 05:18:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Yes, it is a nice idea.


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

#190 2011-07-29 21:13:01

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

Re: Limits!

16)




"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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#191 2011-07-29 21:44:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,809

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

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#192 2011-07-29 21:48:14

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

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

#193 2011-07-29 22:48:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi gAr;


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

#194 2011-07-29 23:25:16

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

Re: Limits!

Hi bobbym,


"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

#195 2011-07-29 23:36:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi gAr;


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

#196 2011-07-29 23:39:00

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

Re: Limits!

Okay, I did the same.

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."

Offline

#197 2011-07-29 23:41:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi gAr;

I have a real old book here that has a nice chart, sometimes Wikipedia makes my eyes hurt.


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

#198 2011-07-29 23:47:41

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

Re: Limits!

Hi bobbym,

What chart is it?


"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

#199 2011-07-29 23:49:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,423

Re: Limits!

Hi;

A chart for indeterminate forms that arise. Old book but I kept it.

You can do that integral fairly easily by series methods. You can get an exact answer.


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

#200 2011-07-29 23:54:03

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

Re: Limits!

Okay.

I derived that integral from the 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

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