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I need an example of a function.

  • Thread starter paalfis
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  • #1
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Member warned about not using the homework template
Give an example of a function f:R2-->R , continuous in (0,0), with partial derivatives in (0,0), but not differentiable in (0,0).

I was thinking in something like f(x,y)=IxyI
 

Answers and Replies

  • #2
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What is the definition of continuous function at a point like (0, 0) ?
 
  • #3
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limit as (x,y)->(0,0) of If(x,y)-f(0,0)I=0
 
  • #4
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I know what this properties mean, I just can't think of a function with partial derivatives in (0,0) but not differentiable in that point.
 
  • #5
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Actually, I think that the function f (x , y) = x1/3y2/3+y1/3x2/3 works fine, am I right?
 
  • #6
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Yeah that seems to work. I plotted it here.

image.jpg


image.jpg
 

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