Answer Happy

Please convert to spherical coordinates (withsimplification) to solve.
(1) Consider the function f: R³ → R given by f(x, y, z) = where k is a positive constant. sin(x + y) cos(z) √x² + y² + z² 0 lim (x,y,z) 0 4 if (x, y, z) (0, 0, 0), if (x, y, z) = (0, 0, 0), (a) Find all values of k> 0 for which f is continuous at the origin. In other words, find all positive real numbers k for which sin(x + y) cos(z) √x² + y² + z² = 0.
(b) Find all values of k> 0 for which fz (0, 0, 0) exists. In other words, find all positive real numbers k for which lim t-0 f(t,0,0)-f(0, 0, 0) t exists and is finite. For each such value, what is fa (0, 0, 0)? (c) What are f(0, 0, 0) and f, (0, 0, 0)? Do those values depend on k?