1. [7 marks] Consider the function f : R2 - R given by 23 f (x, y ) = 12 + 2/2 ' (2, y) * (0, 0) 0, (x, y) = (0, 0) (a) Show that f(x, y) is continuous at (0, 0). (b) Use formal definition of the partial derivatives to find of and of axc ay at (x, y) = (0, 0). (c) Evaluating the appropriate limit determine whether f is differentiable at (0, 0) . (d) Does the linear approximation of f(x, y) in vicinity of (x, y) = (0, 0) exist? Justify your