Question deals with something we didn't exactly learn in class: three-dimensional limits

(1) Consider the function f : R3 > R given by 23 Sin(:.c2 l 9'2) aw): m iflxayazhwm), 0 if (:12, 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, nd all positive real numbers 19 for which _ 213 sin(:.c2 + :92) 11m : 0 (ram>0 (x2 + y2 + 22F; (b) Find all values of k for which fz (0, 0, 0) exists. In other words, nd all positive real numbers k for which f(0303t) _f(03030) Ill tm t exists and is nite. For each such value, what is fz(0, 0, 0)? (c) What are rm, 0, 0) and fy(0, 0, 0)