1. Consider the function: f(x, y) = ylal (a) (2 points) Is f(x, y) continuous at (0, 0)? (b) (4 points) Do the partial derivatives of and of exist at (0, 0)? (c) (4 points) Recall theorem 15.5 from the textbook: Suppose the function f has partial derivatives defined on an open set containing (a, b) with fr and fy continuous at (a, b). Then f is differentiable at (a, b). Do the conditions of this theorem hold for the function f(x, y) = yal at (0, 0)? (d) (6 points) Show the function is differentiable at (0, 0). (e) (4 points) Compute the directional derivative in the direction u = (cos(0), sin(0)) of f at (0,0) (as a function of 0)