3) 7 points - Find the surface area of the surface given parametrically by 7(u, v) = 2 sin u cos vi + 2 sin u sinvj+2cos uk , 0 u π,0 vS2π 3) 7 points - Find the surface area of the surface g...
3) 7 points Find the surface area of the surface given parametrically by
3) 7 points Find the surface area of the surface given parametrically by
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos v)cos ui + (a + b cos v)sin uj + b sin vk, where a > b, 0 2 π, b > 0, and 0 2π u v
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos...
Please solve this question
The image of the parametrization Ф(u, u)-(a . sin(u) . cos(v), b . sin(u) . sin(v), c . cos(u)) with óくa, 0 < u < π, 0 < v < 2π parametrizes an ellipsoid. a) Show that all the points in the image of Ф satisfy the Cartesian equation of an ellipsoid E 2 b) Show that the image surface is regular at all points c) Write out the integral for its surface area A(E), (Do...
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).
Find the first quadratic form of a surface called helicoid, r(u, v)-(u cos v, u sin v, av), where a is a constant parameter. Then find the angle of intersection of lines on the surface of helicoid given by equations u v0, u0.
Find the first quadratic form of a surface called helicoid, r(u, v)-(u cos v, u sin v, av), where a is a constant parameter. Then find the angle of intersection of lines on the surface of helicoid...
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
10. Consider the surface S parameterized by w r= (cos y, sin v, u + sin v), -3 <u <3, 050 < 27 *** (a) Write a linear equation for the tangent plane to the surface at (0,1,1) (b) Compute the surface area of S.
1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0 < u < 2T. (a) Compute Tu, Tu, and Tu X T, (b) Compute
1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0
Consider the area bounded by θ 0 and θ = π/2 and cos θ + sin θ. Calculate this area