2. For each of the following functions, find out whether the given expression can be solved for z in a nonempty, open set V containing (0,0,0). Is the solution differentiable near (O,O)?

(a) xyz + sin(x + y + z) = 0.

(b) x2 + y2 + z2 + ij2xy + 3z + 8) = 2.

(c) xyz(2cosy - cosz) + (z cos x - xcosy) = 0.

(d) x + y + z + g(x, y, z) = 0, where g is any continuously differentiable function that satisfies g(O, 0, 0) = ° and gAO, 0, 0) > 0.