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Can you find this kind of function? (Posted on 2006-08-28) Difficulty: 4 of 5
Can you find a function that is differentiable at the origin but the function itself is not continuous at the origin?

No Solution Yet Submitted by atheron    
Rating: 3.5000 (2 votes)

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Some Thoughts Possible Solution | Comment 9 of 10 |

How about f(x)=x/x? 

Since 0/0 is not defined f(x) is not continous at x=0.

But, f'(x)=lim (t->0) of (((x+t)/(x+t)) - (x/x))/t

=lim (t->0) of ((x+t)x - x(x+t))/((x(x+t))t)

=lim (t->0) of 0/((x(x+t))t)=0

So, f'(x)=0 for all defined x including x=0.

  Posted by gregg on 2006-10-25 00:23:28
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