(1) Consider the function f : R' - R given by z' sin(x2+ 12) f ( x, y, Z) = ( x2 + 12 + 22) k if (x, y, z) # (0, 0, 0), 0 if (x, y, z) = (0, 0, 0), where k is a positive constant. (a) Find all values of k for which f is continuous at the origin. In other words, find all positive real numbers k for which lim z' sin(x2+ 1 ) = 0. (x, y,z)-0 (x2+ 12 + 22) k (b) Find all values of k for which fz(0, 0, 0) exists. In other words, find all positive real numbers k for which lim f(0, 0, t) - f(0, 0, 0) 1 - 0 exists and is finite. For each such value, what is fz (0, 0, 0)? (c) What are fx(0, 0, 0) and fy (0, 0, 0)