Sketch S and compute integral of ω where
![S is the oriented surface given by the parametrization Ф(u, v) (11+1, 112-r ,in) and (u, v) [0.1]х [0,1]](http://img.homeworklib.com/images/fdc34125-7d83-4cef-b55e-0ffb567a71b8.png?x-oss-process=image/resize,w_560)
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S is the oriented surface given by the parametrization Ф(u, v) (11+1, 112-r ,in) and (u, v) [0.1]...
3. Sketch S and compute where S is the part of the cone z-Vx+y* between z-1 andz -3, oriented by ...
3. Sketch S and compute where S is the part of the cone z-Vx+y* between z-1 andz -3, oriented by the unit normal with negative z-component. S is the oriented surface given by the parametrization ф(II,'')-(11+1, 112-r ,uv) and (11, v) E [0.1] x [0.1] S is upper unit hemisphere, oriented by the unit normal pointing away from the origin.
3. Sketch S and compute where S is the part of the cone z-Vx+y* between z-1 andz -3, oriented by...
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...
Compute the differential of surface area for the surface S described by the given parametrization...
Compute the differential of surface area for the surface S described by the given parametrization. ru, v)-(eu cos(v), eu sin(v), uv), D-{(u, v) I o s u s 4,0 s v s 27
Compute the differential of surface area for the surface S described by the given parametrization. ru, v)-(eu cos(v), eu sin(v), uv), D-{(u, v) I o s u s 4,0 s v s 27
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...
Surface D is given by r(u, v) = u, v, u2 + v^2 , above the...
Surface D is given by r(u, v) = u, v, u2 + v^2 , above the solid circle x 2 + y 2 ≤ 2, oriented upwards. The vector field F is (x^2 , xz, y2*z). Set up a double integral with the same value as Z ∂D F · dr, so that the integral is ready to evaluate. Do not evaluate either integral.
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t)...
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
Assume that is the parametric surface r= x(u, v) i + y(u, v) j + z(u,...
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,...
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin...
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin u, v) for (u, v) E D where D = {(u, v) O SUST, SU <3}. Set up the iterated integral, but do not evaluate, the surface area JJsdS (I want the iterated integral for du du, and in that order. Do not even try to evaluate this integral!).
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped...
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0 < u 2, 0 £1 3 Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0 < u 2, 0 £1 3
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0
3. Sketch S and compute where S is the part of the cone z-Vx+y* between z-1 andz -3, oriented by the unit normal with negative z-component. S is the oriented surface given by the parametrization ф(II,'')-(11+1, 112-r ,uv) and (11, v) E [0.1] x [0.1] S is upper unit hemisphere, oriented by the unit normal pointing away from the origin.
3. Sketch S and compute where S is the part of the cone z-Vx+y* between z-1 andz -3, oriented by...
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...
Compute the differential of surface area for the surface S described by the given parametrization. ru, v)-(eu cos(v), eu sin(v), uv), D-{(u, v) I o s u s 4,0 s v s 27
Compute the differential of surface area for the surface S described by the given parametrization. ru, v)-(eu cos(v), eu sin(v), uv), D-{(u, v) I o s u s 4,0 s v s 27
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...
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
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,...
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin u, v) for (u, v) E D where D = {(u, v) O SUST, SU <3}. Set up the iterated integral, but do not evaluate, the surface area JJsdS (I want the iterated integral for du du, and in that order. Do not even try to evaluate this integral!).
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0 < u 2, 0 £1 3
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0
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