Figure 1 Region S bounded above by paraboloid z = 8−x2−y2 and below by paraboloid z = x2y2 Surfaces intersect on the curve x2 y2 = 4 = z So boundary of the projected region R in the x−y plane is x2 y2 = 4 Where the two surfaces intersect z = x2 y2 = 8 − x2 − y2 So, 2x2 2y2 = 8 or x2 y2 = 4 = z, this is the curve atA hyperbolic paraboloid of equation z = a x y {\displaystyle z=axy} or z = a 2 ( x 2 − y 2 ) {\displaystyle z= {\tfrac {a} {2}} (x^ {2}y^ {2})} (this is the same up to a rotation of axes) may be called a rectangular hyperbolic paraboloid, by analogy with rectangular hyperbolasA paraboloid described by z = x ^ 2 y ^ 2 on the xy plane and partly inside the cylinder x ^ 2 y ^ 2 = 2y How do I find the volume bounded by the surface, the plane z = 0, and the cylinder?
Apostila De Matheus Sobre X Y Dl Dx X Y 0 Dl Dy X Y 0 B Docsity
