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#1 2011-06-28 03:27:18

gAr
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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."
 

#2 2011-06-28 03:55:07

anonimnystefy
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Re: Limits!

hi gAr

thanks for opening the topic!
I needed this.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#3 2011-06-28 04:05:45

anonimnystefy
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Re: Limits!

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#4 2011-06-28 04:09:37

gAr
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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."
 

#5 2011-06-28 04:41:34

anonimnystefy
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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 (2011-07-27 20:41:42)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#6 2011-06-28 13:22:37

gAr
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Re: Limits!

Hi anonimnystefy,




Last edited by gAr (2011-06-28 13:23:41)


"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."
 

#7 2011-06-28 13:37:30

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#8 2011-06-28 13:43:55

gAr
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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."
 

#9 2011-06-28 18:42:35

gAr
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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."
 

#10 2011-06-28 21:01:16

anonimnystefy
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Re: Limits!

hi gAr


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#11 2011-06-28 21:08:10

gAr
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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."
 

#12 2011-06-28 21:14:12

anonimnystefy
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Re: Limits!

nope.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#13 2011-06-28 21:29:27

bobbym
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Re: Limits!

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#14 2011-06-28 21:38:37

gAr
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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 (2011-06-28 21:39:40)


"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."
 

#15 2011-06-28 21:47:22

anonimnystefy
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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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#16 2011-06-28 21:56:06

gAr
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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."
 

#17 2011-06-28 22:01:13

anonimnystefy
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Re: Limits!

hi gAr

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#18 2011-06-28 22:08:12

gAr
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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."
 

#19 2011-06-28 22:31:54

anonimnystefy
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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 22:32:04)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#20 2011-06-28 22:48:28

gAr
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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."
 

#21 2011-06-28 23:11:56

anonimnystefy
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Re: Limits!

So how would you do this one?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#22 2011-06-28 23:22:57

gAr
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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."
 

#23 2011-06-28 23:24:19

123ronnie321
Full Member

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Re: Limits!

Hi anonimnystefy,

This one is for you!

 

#24 2011-06-28 23:36:46

anonimnystefy
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Re: Limits!

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

Last edited by anonimnystefy (2011-06-28 23:37:55)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#25 2011-06-28 23:45:53

gAr
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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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