2.2.72 Derivatives and Differentials

Condition: 1. Find the area of determination of the function of two variables \ (z = f (x, y) \). To depict it on the coordinate plane and shake it. 2. Check if the function of two variables satisfies \ (\ quad Z = f (x, y) \ quad \) specified by the differential equation. 1) \ (z = \ sqrt {1-x^{2} -y^{2}}} \) 2) a) \ (z = x \ cdot \ sin \ left (x^{2} -y^{2} \ right), \ quad x^{2} \ cdotot \ frac {\ partial z} {\ partial y}+x y \ frac {\ partial z} {\ partial x} = z y \), b) \ (z = \ cos ^{2} (x+y)+\ ln (x-y), \ frac {\ partial^{2} z} {\ partial x^{2}} = \ frac {\ partial^{2} z} {\ partial y^{2}} \).