The question is complete, including the topic vector Calculus

(1) Consider the function f : R3 - R given by * (ex2 +y? - 1) f ( 2, y, z) = 3 ( ac2 + 92 + 2 2 ) k if ( x , y, z) + (0, 0, 0), 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 2k (ex2 + 32 - 1) (a, y,z) -0 (202 + 32 + 22) k = 0. (b) Find all values of k for which the partials fx (0, 0, 0), fy (0, 0, 0) and fz (0, 0, 0) exists. For each such values, compute fx (0, 0, 0), fy(0, 0, 0) and fz (0, 0, 0)