Find an equation forthe plane tangent to the cone r(r,6)=(r cos 6) i+(r sin 6)] + r k, 20056521; 21: at the point P0 ( 1,152) corresponding to (r,B) = [2?] . Then nd a Cartesian equation for the surface and sketch the surface and tangent plane together. 0 Click here for more information about the plane tangent to a parametrized surface. The tangent plane at a point P0(x,y,z) on a parametrized surface r(r,6) = (r cos 6)i + (r sin 6)] + r k is the plane through P0 normal to the vector rrx re, the cross product ofthe tangent vectors at PO. What is the equation of the tangent plane? = 0 (Type an expression using x, y, and 2 as the variables. Type an exact answer, using radicals as needed.) Use a parametrization to express the area of the surface as a double integral. Then evaluate the integral. The lower portion cut from the sphere x2 + y2 + Z2 = 25 by the cone 2 = 4x2 + y2 Let u = 8 and v = q: and use spherical coordinates to parametrize the surface. Set up the double integral to nd the surface area. [I( )dudv (Type exact answers.) Use a parametrization to express the area of the surface as a double integral. Then evaluate the integral. The portion of the cylinder x2 + y2 =16 between the planes 2 = 5 and z = 6 Let u = z and V: 9 and use cylindrical coordinates to parameterize the surface. Set up the double integral to nd the surface area. [I( )dudv (Type exact answers.)