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#1 2011-06-27 05:27:18

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

Limits!

1)


"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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#2 2011-06-27 05:55:07

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi gAr

thanks for opening the topic!
I needed this.


“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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#3 2011-06-27 06:05:45

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

I'm not sure i know how to do this one but it shoud be e^(1/6).


“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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#4 2011-06-27 06:09:37

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

Re: Limits!

Hi anonimnystefy,

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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#5 2011-06-27 06:41:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi gAr

I still can't seem to get it

All I got is the given expression is the same as

and

Last edited by anonimnystefy (2011-07-26 22:41:42)


“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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#6 2011-06-27 15:22:37

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

Re: Limits!

Hi anonimnystefy,


Last edited by gAr (2011-06-27 15:23:41)


"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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#7 2011-06-27 15:37:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: Limits!

Hi all;

Wunderbar!

I think it is obvious that gAr has the Ramanujan touch! Even his typos are cool.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#8 2011-06-27 15:43:55

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

Re: Limits!

Hi bobbym,

I'm nowhere near Ramanujan!
That typo wasn't deliberate, but glancing at that I too think it's cool!


"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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#9 2011-06-27 20:42:35

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

Re: Limits!

2)


"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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#10 2011-06-27 23:01:16

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

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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#11 2011-06-27 23:08:10

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

Re: Limits!

Hi anonimnystefy,

Have you studied integration?


"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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#12 2011-06-27 23:14:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

nope.


“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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#13 2011-06-27 23:29:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: Limits!

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#14 2011-06-27 23:38:37

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

Re: Limits!

Okay.
I hope you can search about that during your spare time.
Anyway, I'll tell briefly the concept of getting the answer.
Learn during your spare time. Very interesting!

Hi bobbym,

That's correct !

Last edited by gAr (2011-06-27 23:39:40)


"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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#15 2011-06-27 23:47:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi gAr

think i get it.
i have read something on integrals but thats only the basic stuff.For example i wouldn't know how to calculate ∫1/(a^2+x^2)dx


“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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#16 2011-06-27 23:56:06

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

Re: Limits!

Hi anonimnystefy,

That's great!
But before going to integrals, know differentiation clearly.
Otherwise you'll have trouble remembering some results!


"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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#17 2011-06-28 00:01:13

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi gAr

the only problem i have with diff. is i have difficulties when it comes to products and function composition.


“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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#18 2011-06-28 00:08:12

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

Re: Limits!

For example?


"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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#19 2011-06-28 00:31:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

I got confuzed with derivative of:


I got it in the end but a little harder than it maybe should be.

Last edited by anonimnystefy (2011-06-28 00:32:04)


“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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#20 2011-06-28 00:48:28

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

Re: Limits!

I always take logarithms and then take derivative for such problems!
Extra effort is during simplification, but easier than quotient 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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#21 2011-06-28 01:11:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

So how would you do this one?


“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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#22 2011-06-28 01:22:57

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

Re: Limits!

Hi,


"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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#23 2011-06-28 01:24:19

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

Re: Limits!

Hi anonimnystefy,

This one is for you!

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#24 2011-06-28 01:36:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

I think it should be \lim_{x\to-\infty}.

Last edited by anonimnystefy (2011-06-28 01:37:55)


“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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#25 2011-06-28 01:45:53

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

Re: Limits!

Answer exists for -∞ also.


"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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