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#1 2011-11-12 10:42:00

anonimnystefy
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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?


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 2011-11-12 19:43:09

bob bundy
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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 (2011-11-12 19:45:55)


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

#3 2011-11-13 06:45:55

anonimnystefy
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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?


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 2011-11-13 08:34:58

bob bundy
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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

#5 2011-11-13 10:16:14

anonimnystefy
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Re: sgn(x)!!!

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


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 2011-11-13 12:10:15

reconsideryouranswer
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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 2011-11-13 12:12:46

anonimnystefy
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Re: sgn(x)!!!

nice explanation! thanks rya!

i guess sgn(x) can be done similairly.


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 2012-10-27 09:20:51

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 2012-10-27 10:29:54

anonimnystefy
Real Member

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Re: sgn(x)!!!

That looks ok too.


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

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