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

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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### 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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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## #104 2011-06-30 01:01:08

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### 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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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## #106 2011-06-30 01:12:57

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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### 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."

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

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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### 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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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## #119 2011-07-01 04:52:07

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Limits!

Hi anonimnystefy,

"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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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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: 3,479

### 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

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### 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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