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#1 2013-11-28 12:58:21

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Differentiable

A draft page: Differentiable

Is it correct?

Ideas for improvement?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2013-11-28 15:09:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,616

Re: Differentiable

Hi;

Looks good!

Interesting is that  the function sin( 1 / x ) is not differentiable at 0 and neither is x sin( 1 / x ) but x^2 sin( 1 / x ) is!


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.

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#3 2013-11-28 21:45:26

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 606
Website

Re: Differentiable

Some corrections.

The Floor and Ceiling Functions are not differentiable, as there is a discontinuity at each jump.

More precisely, they are not differentiable only at integer values of x. (If x is not an integer they are perfectly differentiable at x.)

Similarly the function so y=x[sup](1/3)[/sup] is only not differentiable at the origin; elsewhere it is differentiable.

The y=1/x and  y=sin(1/x) are not defined at the origin so it makes no sense to ask whether they are differentiable there. To be differentiable at a certain point, the function must first of all be defined there!

And the last part:

But a c̶o̶n̶t̶i̶n̶u̶o̶u̶s̶ ̶f̶u̶n̶c̶t̶i̶o̶n̶ function that is continuous at a certain point might not be differentiable at that point, for example the absolute value function is actually continuous (though not differentiable) at the origin.

Last edited by Nehushtan (2013-11-28 22:49:53)


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#4 2013-11-28 23:30:24

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Re: Differentiable

Thanks bobby and Nehushtan.

May I use some of your wording Nehushtan?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2013-11-29 04:22:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,616

Re: Differentiable

May I use some of your wording Nehushtan?

I certainly would, JFF could not have said it better.

In post #2 I left out the other part of the function definition. I should have said,

f(x) is differentiable at 0 according to the SE. x^2 sin( 1/ x ) would not be because it is not defined at 0.


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.

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#6 2013-11-30 01:04:55

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,116

Re: Differentiable

hi MathsIsFun

The page looks good to me.  Well done!  smile

Bob


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

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