(1) Consider the function f: R3 > R given by sin(mk + y'\") (305(2) ,/2 2 2 f($ay:z): 112 +3, +2 0 if (33y! 2) : (D! 01' 0)? 1f (53;. 3;, Z) # (0: 0: 0): where k is a positive constant. (3) Find all values of k > 0 for which f is continuous at the origin. In other words, nd all positive real numbers 11: for which 1.1m sin(3:k +yk)cos(z) : [m,y,z)>0 /332 _|_ y2 _|_ 32 0. (b) Find all values of k > 0 for which fx (0, 0, 0) exists. In other words, find all positive real numbers k for which f (t, 0, 0) - f(0, 0, 0) lim t-+0 t exists and is finite. For each such value, what is fx (0, 0, 0)? (c) What are fz (0, 0, 0) and fy (0, 0, 0)? Do those values depend on k