a and b.

(1) Consider the function f : R3 - R given by zk (ex-ty - 1 ) if (x, y, z) # (0, 0, 0), f ( x, y, Z) = 3 (x2 + 12 + 22 ) 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 zk (ex-ty - 1) lim = 0. (x, y, z)-0 (x2+ 12+ z2)k Hint: if you want, you can use the fact that el - 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 f= (0, 0, 0)