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

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

### Re: Limits!

Hi bobbym,

Okay.
It simplifies finding some integrals.

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

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

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

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

### Re: Limits!

Hi,

Did you see this before? Good examples to evaluate some famous integrals:

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

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

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

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

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

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

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

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

### 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
The knowledge of some things as a function of age is a delta function.

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## #183 2011-07-28 03:27:53

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

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

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

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

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

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

### Re: Limits!

Okay gAr, see you then.

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.

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

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

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

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

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

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

### Re: Limits!

Yes, it is a nice idea.

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.

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

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

### 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: 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.

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

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."

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

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

### Re: Limits!

Hi gAr;

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.

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

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

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

### Re: Limits!

Hi gAr;

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.

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

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

### 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."

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

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

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

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

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

### 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."

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

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

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

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

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

### 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."

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