a and b only.

(1) Consider the function f : R' - R given by z' sin(x2 + 12) if (x, y, z) # (0, 0, 0), f ( x, y, Z ) = 3 (x2 + 12 + 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 z' sin(x2 + 12) (x, y, z)-0 (x2 + 12 + 22)k = 0. (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)