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...

Question

Question

Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(

math calculus

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Area elu 2n

Add a comment

Answer 2

Similar Homework Help Questions

Find the area of the surface over the given region. Use a computer algebra system to verify your results. Find the area of the surface over the given region. Use a computer algebra system to ver...

Find the area of the surface over the given region. Use a computer algebra system to verify your results. Find the area of the surface over the given region. Use a computer algebra system to verify your results.
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 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 given parametrically by 7(u, v) = 2 sin u cos vi + 2 sin u sinvj+2cos uk , 0 u π,0 vS2π
The image of the parametrization Ф(u, u)-(a . sin(u) . cos(v), b . sin(u) . sin(v), c . cos(u)) w...

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...

Find the first quadratic form of a surface called helicoid, r(u, v)-(u cos v, u sin v, av), where...

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...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos...

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...
both questions Use a computer algebra system and the fact that the centroid of the region having area A bounded by the simple closed path C is xd to find the centroid of the region. R: region bou...

both questions Use a computer algebra system and the fact that the centroid of the region having area A bounded by the simple closed path C is xd to find the centroid of the region. R: region bounded by the graphs of y -x and y 3 sin θ and outside the circle x-2 cos θ, y-2 sin θ, Evaluate the line integral Let R be the region inside the ellipse x-4 cos θ, y (3x2y + 7) dx +...

1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0 < u < 2T. (a...

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
7. Find an equation of the tangent plane to the given parametric surface r(u, v) =...

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).
11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y)...

11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y) by х — 2иv, y — u? — u? for (и, v) € [0, оо) х [0, оо) 1 u = 1, u 2' (a) Sketch in the ry-plane the curves given u = 2. Then sketch in 1 v = 1, v = 2. Shade in the region R the xy-plane the curves given v = 2' bounded by the curves given by...

all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B)...

all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...

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...

Homework Answers

Add Answer to:
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...

Post as a guest

Earn Coins

Find the area of the surface over the given region. Use a computer algebra system to verify your results. Find the area of the surface over the given region. Use a computer algebra system to ver...

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...

The image of the parametrization Ф(u, u)-(a . sin(u) . cos(v), b . sin(u) . sin(v), c . cos(u)) w...

Find the first quadratic form of a surface called helicoid, r(u, v)-(u cos v, u sin v, av), where...

5. In class we saw that the function r(u, v) = (sin u, (2 + cos...

both questions Use a computer algebra system and the fact that the centroid of the region having area A bounded by the simple closed path C is xd to find the centroid of the region. R: region bou...

1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0 < u < 2T. (a...

7. Find an equation of the tangent plane to the given parametric surface r(u, v) =...

11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y)...

all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B)...

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...

Homework Answers

Add Answer to: 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...

Post as a guest

Earn Coins

Add Answer to:
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...