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#451 2012-02-19 14:33:36

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

Re: Limits!

Hi bobbym,

What is the limit of a_n as n approaches infinity, with a being any real number.


"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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#452 2012-02-19 14:37:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

Very good! You found the link, I was hiding it!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#453 2012-02-19 14:49:00

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

Re: Limits!

Thanks!
Do you want me to erase the link?


"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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#454 2012-02-19 16:16:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

No, that is okay. I was just teasing him.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#455 2012-02-19 16:33:29

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

Re: Limits!

Okay.


"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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#456 2012-02-19 20:52:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

Hi gAr;

Did you know to do that one before you found the link?


Hi anonimnystefy;

See post #450.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#457 2012-02-19 21:25:30

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

Re: Limits!

Hi bobbym,

I tried for sometime, but didn't get the solution. Then I searched for the link.


"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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#458 2012-02-19 21:51:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

Hi;

I was unable to get it either.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#459 2012-02-19 22:33:43

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

Re: Limits!

Summations with flooring and ceiling are a bit difficult for 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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#460 2012-02-20 00:16:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

I agree, it is very hard to eliminate them.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#461 2012-02-20 02:48:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

hi bobbym


“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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#462 2012-02-20 05:17:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

Hi;

No problem is too easy!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#463 2012-02-20 05:43:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

hi bobbym


“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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#464 2012-02-20 05:46:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

Very good!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#465 2012-02-20 05:49:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

hi bobbym

next one?

and if you can,please check my attempt at the series #17 problem.tell me if it's good at all.if not i want to change my direction so that i don't waste my time on wrong attempts. smile


“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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#466 2012-02-20 05:55:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#467 2012-02-20 06:04:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

hi bobbym

my new friend Maxima says it's


“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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#468 2012-02-20 06:12:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

What do you say it is?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#469 2012-02-20 06:13:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

hi bobbym


“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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#470 2012-02-20 06:15:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

How do you go about getting such an answer?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#471 2012-02-20 06:33:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

hi bobbym

i'm not sure.maybe because e/x tends to zero when x goes to infinity,and 0^'infinity' tends to zero? i'm just guessing because i tried to do the l'Hopital's rule,but i got some pretty nasty functions.


“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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#472 2012-02-20 06:35:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

Do you at least have some empirical evidence?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#473 2012-02-20 06:43:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

hi bobbym

wolfram won't work it out for x=100 or x=1000. think there's no sense in going larger.


“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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#474 2012-02-20 06:50:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Limits!

Did you know that Maxima can do arithmetic that dwarfs Mathematica's puny efforts.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#475 2012-02-26 04:20:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Limits!

Hi bobbym

I haven't done this on Maxima yet, but I'm sure that the answer is 0.

maybe another way could be using a substitution y=e^x.


“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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