10. The surface described by r(u, v) = cosu i + sinu cosv j + sinu...
Question 2. Define σ: R2-R by σ(u,t)-(u+cosu, sinu, u), and let S be the image of σ. (1) Show that S is a ruled surface. (2) Give a quadratic equation for S, and show S is a quadric. (3) Show that S is an elliptic cylinder, so that a cross section of S perpendicular to the rulings is an ellipse. What are the lengths of its axes? Question 2. Define σ: R2-R by σ(u,t)-(u+cosu, sinu, u), and let S be...
Assume that is the parametric surface r= x(u, v) i + y(u, v) j + z(u, v) k where (u, v) varies over a region R. Express the surface integral 116.3.2) as as a double integral with variables of integration u and v. a (x, y) a(u, v) du dy ru Хry dy du l|ru Xr, || f (x (u, v),y(u, v),z (u, v)) 1(xu, Wsx,y,z) Mos u.v.gou,» @ +()*+1 li ser(u, v),y(u, v),z (u, v) Date f (u, v,...
5. Suppose σ is a parametric surface with vector equation r(14. u) x (u, u)i + y(u, u)j + z(u, v)k If σ has no self-intersections and σ 1s smooth on a region R in the uu-plane, then the surface area of ơ is given by 5. Suppose σ is a parametric surface with vector equation r(14. u) x (u, u)i + y(u, u)j + z(u, v)k If σ has no self-intersections and σ 1s smooth on a region R...
1. Who's that surface? Consider the function Flu, y) = (v cosu, v sin u, u), 0 Su<27, -2 SU <2. The goal of this problem is to figure out what surface this function parametrizes! (a) Find a parametrization of the coordinate curve with u held constant as u = u. Plot a couple of these curves in 3D to see what they look like. (b) Find a parametrization of the coordinate curve with v held constant as v =...
How can I answer by maple 6. Consider the surface S described by r(u, ucos v, u sin v,1-2> (a) Graph the surface S for 0 u 2 and 0 (b) Identify the surface S thus obtained. u .
(2) Let S be the surface parametrized by r(u, v) = (u? – 12)i + (u + v)j + (u? + 3v)k. (a) Find a normal vector to S at the point (3,1,1). (b) Find an equation of the tangent plane to S at (3, 1, 1).
The tangent plane at a point Po(f(uo.VO) 9 (uo.vo) h(uo,VO)) on a parametrized surface r(u,v) = f(u,v) i + g(u,v) j+h(u, v) k is the plane through P, normal to the vector ru (uo.VO) XIV(40.VO) the cross product of the tangent vectors ru (uo. Vo) and rv (uo.VO) at Pg. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. (573 15...
Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 9) i + (v3 + 6u) j + (u + 2v) k , at the point (10, 5, −1). Write the equation in the form ax + by + cz + d = 0, where a, b, c, and d have no common factors. Then enter the values of a, b, c, and d (in that order) into the answer box below, separated...
7. Find an equation of the tangent plane to the given parametric surface r(u, v) = uvi+u sin(n)j + v cos(u)k, at u = 0, v = . 8. Find the area of the part of the surface 2 = 2 + 5x + 2y that lies above the triangle with vertices (0.0), (0,1), and (2,1).
can you please give me a detailed explained answer. I'm struggling with this topic. like and comment are rewarded for clear answers. (b) Consider a conical surface S described by r(u, u) = u cos uz + u sin uit (1-u) k with an (i) Sketch the surface in the coordinate system defined by the axes i, j, k and the origin. (ii) Find OuT x o,r (ii) Evaluate the fluxJs F ds where the vector field F ri +...