Let S be the surface given by x² + y²+2z² = 1, x > 0, y ≥ 0, z ≥ 0. Find the flux of (z, 0, 0) through S, oriented away from the origin.

Find the point(s) on the surface z? (10, 8, 0). = xy+1 which are closest to the point List points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1), (2,0, 3)).

The surface z = x² - y² and the surface ryz = -30 intersect along a curve in R³. Find a vector tangent to this curve at the point P = (-3,2,5). Hint: such a vector is parallel to tangent planes at P to both surfaces.

1. Find a vector which is tangent to the curve of intersection of the surfaces z = x? – y? and xyz + 30 = 0 at the point (-3,2, 5). -