Find a parametrization of the surface. The portion of the sphere x² + y2 + z...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
section 16.6 Use a parametrization to find the flux SSFor Fón do across the surface in the given direction. F= - xi – yj + 3z?k outward (normal away from the z-axis) through the portion of the cone z = Vx² + y2 between the planes z = 3 and z = 4. The flux is (Type an exact answer, using a as needed.)
Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show how you arrived at your answer. Hint: It is often helpful to construct your parametrization using (a) cylindrical coordinates, (b) spherical coordi- nates, or (c) by using a parametrization such as (:2, y, 2) = (u, v, f(u, v)) for the surface 2= f(, y). (a) The portion of the sphere x² + y2 + z2 = 9 that is above the cone z...
Use a parametrization to find the flux SSF Fondo of F=2zk across the portion of the sphere x² + y2 +22=awhere z is positive in the direction away from the origin. The flux is (Type an exact answer in terms of t.)
Obtain a parametrization for the surface z = Vx2 + y2, z < 5. Answer 10 Points r(s, t) = (scost, ssint, t), 0 SS < 5,0 <t< 21 or(s, t) = scost, ssint, s2), 0 <<5,0 < t < 21 r(s, t) = (scost, ssint, s), 0 <3 < 5,0 < t < 2n r(s, t) = (scost, ssint, s), 0 < s < 21,0 <t<5
find the surface area of that portion of the sphere x^2+y^2+z^2 = 25 that is below the xy-plane and within the cylinder x^2+y^2=4 5. [10 Marks] Find the surface area of that portion of the sphere x2 + y2 2-25 that is below the ry-plane and within the cylinder 2 -4
Let Surface S be that portion of the paraboloid z = x2 + y2, which lies between the planes z = 4 and z = 25. Find the Area of S.
1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral 1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral
Find the area of the surface. The portion of the sphere x2 + y2 + z2 = 625 inside the cylinder x2 + y2 = 400 d Help? Read It Talk! Talk to a Tutor Tutor
Let Surface S be that portion of the sphere x2 + y2 + z2 = 9, which is above the plane z = 1. Parametrize this surface and write your final answer in vector function notation.