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#326 2012-02-16 09:36:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Correct! Wanted to see if you were sure.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#327 2012-02-16 09:36:49

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

tongue you sneaky little... big_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
The knowledge of some things as a function of age is a delta function.

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#328 2012-02-16 09:43:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#329 2012-02-16 10:00:18

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

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

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#330 2012-02-16 10:03:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Correct!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#331 2012-02-16 10:06:09

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

hi bobbym

why are you giving these easy ones?


“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.

Offline

#332 2012-02-16 10:10:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#333 2012-02-16 10:17:09

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

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

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#334 2012-02-16 10:17:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Not true.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#335 2012-02-16 10:35:24

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

no?but wolfram said that they don't converge.


“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.

Offline

#336 2012-02-16 10:36:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

What did you enter?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#337 2012-02-16 10:45:12

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

is the ans 0?


“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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#338 2012-02-16 10:46:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Yes, and there is a very good argument for that.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#339 2012-02-16 10:50:49

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

and that is?


“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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#340 2012-02-16 10:57:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Do you agree that we can write the above limit in this more convenient form:


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#341 2012-02-16 11:03:51

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

yes...


“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.

Offline

#342 2012-02-16 11:07:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Have you heard of Stirling's formula or approximation?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#343 2012-02-16 11:14:42

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

no,but i know that e^n is O(n^(n+1/2)) big_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
The knowledge of some things as a function of age is a delta function.

Offline

#344 2012-02-16 11:19:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Okay, Stirling's formula was discovered by James Stirling and is a very good approximation for factorials. It is used quite often in many fields of mathematiocs.

1)First convince yourself that

f(100) is a good approximation of 100!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#345 2012-02-16 11:33:21

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

ok


“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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#346 2012-02-16 11:41:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Now it is important to understand that

but more importantly

This means that Stirling's formula becomes a better and better approximation of n! the larger n gets.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#347 2012-02-16 11:43:57

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

ok.


“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.

Offline

#348 2012-02-16 11:46:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

Remember the result in #340?

and Stirlings formula?

Does not the RHS of 1) look like the LHS of 2 inverted?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

Offline

#349 2012-02-16 11:49:24

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: Limits!

it does.so our limit is:

Last edited by anonimnystefy (2012-02-16 11:49:51)


“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.

Offline

#350 2012-02-16 11:52:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,249

Re: Limits!

That is close:


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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