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#1 2013-11-12 08:32:55

anonimnystefy
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Function sign

Has anyone got an idea about getting the sign of this function:


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

#2 2013-11-13 03:48:30

gAr
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Re: Function sign

Hi,

It's negative for x>1, but what was the question?


"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."

#3 2013-11-13 14:19:51

anonimnystefy
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Re: Function sign

Hi gAr

I managed to get that result as well, but in a very complicated way, which is surprising, since it is a book problem.

The function comes from analysing a different function

for monotonity.


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 2013-11-13 16:16:47

gAr
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Re: Function sign

Hi anonimnystefy,

Okay, I only plotted it, nothing else.


"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 2013-11-13 23:21:25

anonimnystefy
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Re: Function sign

So, do you have any ideas?


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 2013-11-14 05:06:07

gAr
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Re: Function sign

We can see that x^2-1 increases faster than x log x, for x>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."

#7 2013-11-14 08:07:44

anonimnystefy
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Re: Function sign

But, what about the -x^2log(x) term?


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

#8 2013-11-14 16:59:49

gAr
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Re: Function sign

I was talking about the equation in #3


"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 2013-11-15 08:20:26

anonimnystefy
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Re: Function sign

Ah, I see. But, how exactly do I show that it is decreasing.


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

#10 2013-11-16 04:57:10

gAr
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Re: Function sign

Well, I don't know, inequalities is in my todo list!


"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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