Problem 2. Consider the two parametrized curves r(t) = (1+,2-t,t + 382 – 4t + 4)...
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...
Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 4). You don't have an equation for S but you know that the curves r1()(3 2t, 1 - t2,4 5t+t2) r2(u) (2u2, 2u3 1, 2u 2) both lie on S. Find an equation of the tangent plane at P. Find an equation of the tangent plane to the given surface at the specified point. = 4x2y2-9y, (1, 4, 16) z...
4. (1 pt) Calculate Tu, T, and n(u, v) for the parametrized surface at the given point Then find the equation of the tangent plane to the surface at that point Ф(и, у) %3D (2и + v, и — 4v, 5и); Ти The tangent plane: V u=4, v6 , n(u,v) TV =9z
(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...
3. Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1,3). You don't have an equation for S but you know that the curves r(t) = (3 + 3t, 1-t2,3 - 5t + t2) rz(t) = (2+u, 2u3 – 1,2u + 1) both lie on S. Find an equation of the tangent plane at P.
Suppose you need to know an equation of the tangent plane to a surface S at the point P(4, 1, 3). You don't have an equation for S but you know that the curves (t) = (4 + 36, 1-2,3 - 4 +12) rz(u) = (3 + 22, 203 - 1, 2u + 1) both lie on S. Find an equation of the tangent plane at P. 24x + 14y + 162 - 158 = 0 % Need Help? Read...
(10') Consider the equation Cut #cut = 1, 2 & R. (a) Find the characteristic curves. Sketch two curves on the t-x plane. (b) Define the characteristic coordinates. (c) Solve the equation with initial condition u(x,0) = x2 + 1.
(1 point) Consider the surface with parametric equations r(s, t) = (st, s +t, s – t). A) Find the equation of the tangent plane at (2,3,1). B) Find the surface area under the restriction sa + t2 <1
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...