1. (10 分) Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = x² + y² + z² subject to the constraints y - z = 1 and z² - 2x² = 1.

2. (10 分) Let E be the solid bounded by the paraboloid z =- x² + y² and the surface z = and let S be the boundary surface of E, given with positive (outward) orientation. Sketch the solid E and use the Divergence Theorem to find ∬ F ⋅ dS for the vector field F(x, y, z) = (x³, y³, 3xy).