7. (12 分) The usual way to evaluate the improper integraldx (from 0 to ∞) is first to calculate its square: dxdy (double integral from 0 to ∞ for both x and y). Evaluate the integral and solve the resulting equation for I.

(a) (8 分) Find the value of at the point (1, 1, 1) if the equation

xy + z³x - 2yz = 0

defines z as a function of the two independent variables x and y and the partial derivative exists.