Sunday, May 28, 2017

calculus - example of discontinuous function having direction derivative


Is there a function (non piece-wise unlike below) which is discontinuous but has directional derivative at particular point? I have a manual that says the function has directional derivative at (0,0) but is not continuous at (0,0). f(x,y)={xy2x2+y4 if x00 if x=0


Can anyone give me few examples which is not defined piece wise as above?


Answer



f(x,y)=lim


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