Question: Exercise 3 . 1 . Let f : R 2 R be defined by f ( x , y ) = { x y 2

Exercise 3.1. Let f:R2R be defined by
f(x,y)={xy2x2+y2if(x,y)(0,0)0if(x,y)=(0,0)
Show that all the directional derivatives of f exist at (0,0) but f is not differentiable at (0,0).
Exercise 3 . 1 . Let f : R 2 R be defined by f (

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