Let g(x, y) = .
(a) Is g continuous at (0, 0)?
(b) Calculate ∂g/∂x and ∂g/∂y when xy ≠ 0.
(c) Show that gx (0, 0) and gy(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)?
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