1. We consider the following function: f(x, y) =ITV si (I, y) + (0,0) si (I, y) = (0,0) 1- (10 points): Show that f is continuous at (0, 0). 2- (20 points): Calculate the functions fx (x, y) and fy (x, y) (pay attention to the case (x, y) = (0; 0) ). 3- (10 points): Is fx continuous at point (0, 0) ? 2. Let f be the function of two variables given by: f(I, y) = = ray 78 4 72 Si (1, y) + (0,0) Show that the function f has no limit at (0; 0).3. We consider the function f : 2 - R defined by: f(x, y) = Perp(y) 1- (18 points): Calculate the partial derivatives of f of order at most 2. 2- (12 points): Calculate the directional derivative of f at points (0, 0) in the direction (1, 1). 3- (15 points): Let : - I be the function defined by: $(t) = f(vt, log(t)) Calculate the derivative of d for all t E ]0, too[