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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,626

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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 pointmight not be differentiableat 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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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,626

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

hi MathsIsFun

The page looks good to me. Well done!

Bob

Children are not defined by school ...........The Fonz

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

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