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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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

#346 2012-02-16 11:41:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,697

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Online

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