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#1 2011-11-11 11:42:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

sgn(x)!!!

hi guys

i was wondering what derivatives of |x| and sgn(x) are.i thought of something but i got that they were sgn(x) and 0 respectfully.i think something is wrong here.What?


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#2 2011-11-11 20:43:09

bob bundy
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Registered: 2010-06-20
Posts: 6,269

Re: sgn(x)!!!

hi Stefy,

Haven't 'spoken' to you in a while.  Hope you are well.   smile

Derivatives have to be 'well defined'.  Specifically, this breaks down where the left limit isn't the same as the right limit.

So neither have a  defined value at x = 0.

For |x|           the deriv = 1 for x > 0       and         -1 for x < 0.

How are you defining sgn(x) ?

If you mean         1 when x > 0         and          -1 when X < 0,         then zero is correct. 

As this function is discontinuous at x = 0,   I think you must exclude x = 0 from this derivative even though the value is the same either side of zero.

Bob

Last edited by bob bundy (2011-11-11 20:45:55)


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#3 2011-11-12 07:45:55

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: sgn(x)!!!

hi bob

yes,i have been occupied by school and my subjects.this was a crazy week.i'm glad it's over,but there is next week exams and i have physics, analysis and in the one after i have geometry and programming. very busy weeks! smile

anyway,if i gave the restriction x<>0 then would my answers be correct?


“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 2011-11-12 09:34:58

bob bundy
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Registered: 2010-06-20
Posts: 6,269

Re: sgn(x)!!!

hi Stefy

Yes, that's what I think.

Good luck in the exams (not that you need it .. I'm sure you'll do brilliantly)

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2011-11-12 11:16:14

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: sgn(x)!!!

ok thanks for the help,and could sure use luck!I'm not sure about that brilliantly!


“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 2011-11-12 13:10:15

reconsideryouranswer
Member
Registered: 2011-05-11
Posts: 172

Re: sgn(x)!!!

anonimnystefy wrote:

i was wondering what derivatives of |x| and sgn(x) are.
i thought of something but i got that they were sgn(x) and 0
respectfully.i think something is wrong here.What?






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#7 2011-11-12 13:12:46

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: sgn(x)!!!

nice explanation! thanks rya!

i guess sgn(x) can be done similairly.


“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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#8 2012-10-26 10:20:51

zetafunc.
Guest

Re: sgn(x)!!!

reconsideryouranswer wrote:
anonimnystefy wrote:

i was wondering what derivatives of |x| and sgn(x) are.
i thought of something but i got that they were sgn(x) and 0
respectfully.i think something is wrong here.What?





Sorry for the bump, but could you not just say




?

#9 2012-10-26 11:29:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: sgn(x)!!!

That looks ok too.


“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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