1. Generalize the definition of partial derivatives from two variables as done in class to n variables for any n > 2. 2. Generalize the definition of differentiability from two variables as done in class to n variables for any n > 2. of and ayor 3. Find aray of at (0, 0) where xy(x2 -y2) f(x, y) = x2ty2 if (x, y) # (0,0) 0 if (x, y) = (0,0) Are they equal? 4. Let xy2 f(x, y) = 3 if (x, y) # (0,0) if (x, y) = (0,0) Show that Of/Ox and Of /dy exists at (0, 0) but f is not differentiable at (0, 0). (Hint: You may use the theorem saying differentiability = continuity.) 5. Show that 1 T = Vac2 + y2 satisfies the equation Tax + Tyy = 13