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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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re: Possible Solution -- fallacy Comment 10 of 10 |
(In reply to Possible Solution by gregg)

That doesn't work, Gregg.  If the function is not defined at the origin, then I think that it is automatically not differentiable.

The problem in your posting is

lim (t->0) of 0/((x(x+t))t) is not equal to zero if x = 0,

because 0/((x(x+t))t) is undefined for all values of x, so the limit is also undefined.

 
  Posted by Steve Herman on 2006-10-25 12:25:53

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