4. (1 pt) Calculate Tu, T, and n(u, v) for the parametrized surface at the given...
Calculate Tr, T. and N(r, θ) for the parametrized surface at the given point. | I θ . r ., G(r, θ)-(r cos(9), r sin(θ), 1-r2); 16' 4 6' 4 6' 4 Find the equation of the tangent plane to the surface at that point. Calculate Tr, T. and N(r, θ) for the parametrized surface at the given point. | I θ . r ., G(r, θ)-(r cos(9), r sin(θ), 1-r2); 16' 4 6' 4 6' 4 Find the equation...
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...
webwork math233 17742 huang s19 16.4 parametrized surfaces /1 16.4 Parametrized surfaces: Problem 1 Problem List Next Problem Previóus Problem (1 point) Show that Ф (u, u)-- (9u t-3, u-u, 17u t u) parametrizes the plane 2x-y-z--6. Then (a) Calculate Tu. T. and n(u, v) (b) Find the area of S-D(D), where D = (mu) : 0 < u < 6,0 < u < 7 (c) Express f(x, y, 2 yz in terms of u and v and evaluate JTs...
(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).
Problem 2. Consider the two parametrized curves r(t) = (1+,2-t,t + 382 – 4t + 4) and r(u) = (u?, 3 - u, u' + 22 - 6u + 8), where t and u are in R. (a) Find the coordinates of the point of intersection P of the two curves. (b) The curves traced out by ry and r2 lie on a surface S. Find an equation of the tangent plane to the surface S at the point P...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds- 1 point)...
1) Assume you are given the surface S with equation 2 1- (a) Find the equation of the tangent plane to S at the point (V6, 1) (b) Find a point on the surface S so that the tangent plane to S at that point contains the point (3,0, 0). (c) Give an equation for and geometrically describe the set of points on S so that the tangent plane to S at those points contains the point (3, 0,0). 1)...
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).
Let M be the surface parametrized by T: (1, 0) R → R3 (u, v) = (ucov, usin 0,0 + 8"}2+1]" d) 1 Compute the mean curvature of M.
Let F = <z, 0, y> and let S be the oriented surface parametrized by G(u, v) = (u2 − v, u, v2) for 0 ≤ u ≤ 6, −1 ≤ v ≤ 4. Calculate the normal component of F to the surface at P = (24, 5, 1) = G(5, 1).