Partial derivatives and differentiability (Sect. 14.3 ...

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Remark: Here is a discontinuous function at (0,0) having partial derivatives at (0,0). Example (a) Show that f is not continuous at (0,0), where f (x,y) = 2xy x2 + y2 (x,y) 6= (0 ,0), 0 (x,y) = (0,0). (b) Find f x(0,0) and f y (0,0). Solution: (a) Choosing the path x = 0 we see that f (0,y) = 0, so lim y→0 f (0,y) = 0. Choosing the path x = y ...

  Functions, Discontinuous, Discontinuous function