(1) Consider the function f : R' - R given by zk (exty - 1 ) if ( x, y, z) # (0, 0, 0), f ( x, y, Z ) = 3 (x 2 + 2 + z2) k 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 zk (exty - 1) . = 0. (x, y, z)-0 (x2+ 2 + 22)k Hint: if you want, you can use the fact that e' - 1 ~ t, as t - 0. (b) Find all values of k for which the partials fx (0, 0, 0), fy (0, 0, 0) and fz (0, 0, 0) exist. For each such value, compute fx (0, 0, 0), fy (0, 0, 0) and fz(0, 0, 0)