Let g(x, y) = . (a) Is g continuous at (0, 0)? (b) Calculate ∂g/∂x and ∂g/∂y when xy...

Let g(x, y) = .

(a) Is g continuous at (0, 0)?

(b) Calculate ∂g/∂x and ∂g/∂y when xy ≠ 0.

(c) Show that g_x (0, 0) and g_y(0, 0) exist by supplying values for them.

(d) Are ∂g/∂x and ∂g/∂y continuous at (0, 0)?

(e) Does the graph of z = g(x, y) have a tangent plane at (0, 0)? You might consider creating a graph of this surface.

(f) Is g differentiable at (0, 0)?