Tuesday, March 5, 2019

calculus - Example of a continuous function which is not smooth



I need a function which is continuous but not smooth ( not a C).



Smooth functions are those whose derivatives of all order exists. For example f(x)=ex is a smooth function while f(x)=|x| is not smooth as derivative at 0 does not exist.


But what I require is functions in from Rn to Rm.


For simplicity it is enough to give functions from R2 to R2. I have examples of discontinuous functions from R2 to R2 , like xyx2+y2 which is not continuous at (0,0).

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