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

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

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
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,178

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

Nehushtan
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From: London
Registered: 2013-03-09
Posts: 613
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: 7,535

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: 86,178

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,374

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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