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5. Suppose σ is a parametric surface with vector equation r(14. u) x (u, u)i + y(u, u)j + z(u, v)...
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,...
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).
Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2...
Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 9) i + (v3 + 6u) j + (u + 2v) k , at the point (10, 5, −1). Write the equation in the form ax + by + cz + d = 0, where a, b, c, and d have no common factors. Then enter the values of a, b, c, and d (in that order) into the answer box below, separated...
The tangent plane at a point Po(f(uo.VO) 9 (uo.vo) h(uo,VO)) on a parametrized surface r(u,v) =...
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...
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 : -...
(2) Let S be the surface parametrized by r(u, v) = (u? – 12)i + (u...
(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).
(c) Let L be the line given by the parametric vector equation r=ro + tv, where...
(c) Let L be the line given by the parametric vector equation r=ro + tv, where ro = i +2j + 3k and v = -i+j - k, and let P be the plane given by the vector equation (r-ru).n=0, where rı = 3j + 3k and n=i+ 3j+k. Find the point where L and P intersect.
Give a parametric description of the form r(u, v) = (x(u,v),y(u,v),z(u,v)) for the following surface. The...
Give a parametric description of the form r(u, v) = (x(u,v),y(u,v),z(u,v)) for the following surface. The cap of the sphere x² + y2 + z = 36, for 3/3 sz56 Select the correct choice below and fill in the answer boxes to complete your choice. (Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 21. Type exact answers in terms of ..) A. Fu.v) = (6 sin u cos V,6 sin...
79. Parametrised Surface 1. Consider the parametrised surface defined by: x 2u, y u2+ v (a) Find a vector normal to the...
79. Parametrised Surface 1. Consider the parametrised surface defined by: x 2u, y u2+ v (a) Find a vector normal to the surface in terms of u and v. (b) For what values of u and v is the surface smooth? (c) Find the equation of the tangent plane to the surface at (0,1, 1)
79. Parametrised Surface 1. Consider the parametrised surface defined by: x 2u, y u2+ v (a) Find a vector normal to the surface in terms...
5. A surface is parameterized by u and v as xacosucosv y bsinucosv z csinv Here...
5. A surface is parameterized by u and v as xacosucosv y bsinucosv z csinv Here 0su<2r, -/2<v< /2, a, b and c are nonzero constants. (a) Express the surface equation in the form f(x, y,z) 1. Find f(x,y,2) (b) Calculate the gradient of the f mentioned above and find the unit normal vector n ar ar (c) Calculate the (un-normalized) normal vector N=- X Cu xr, and normalize it to get the unit normal vector n again. Notation and...
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,...
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).
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...
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 : -...
(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).
(c) Let L be the line given by the parametric vector equation r=ro + tv, where ro = i +2j + 3k and v = -i+j - k, and let P be the plane given by the vector equation (r-ru).n=0, where rı = 3j + 3k and n=i+ 3j+k. Find the point where L and P intersect.
Give a parametric description of the form r(u, v) = (x(u,v),y(u,v),z(u,v)) for the following surface. The cap of the sphere x² + y2 + z = 36, for 3/3 sz56 Select the correct choice below and fill in the answer boxes to complete your choice. (Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 21. Type exact answers in terms of ..) A. Fu.v) = (6 sin u cos V,6 sin...
79. Parametrised Surface 1. Consider the parametrised surface defined by: x 2u, y u2+ v (a) Find a vector normal to the surface in terms of u and v. (b) For what values of u and v is the surface smooth? (c) Find the equation of the tangent plane to the surface at (0,1, 1)
79. Parametrised Surface 1. Consider the parametrised surface defined by: x 2u, y u2+ v (a) Find a vector normal to the surface in terms...
5. A surface is parameterized by u and v as xacosucosv y bsinucosv z csinv Here 0su<2r, -/2<v< /2, a, b and c are nonzero constants. (a) Express the surface equation in the form f(x, y,z) 1. Find f(x,y,2) (b) Calculate the gradient of the f mentioned above and find the unit normal vector n ar ar (c) Calculate the (un-normalized) normal vector N=- X Cu xr, and normalize it to get the unit normal vector n again. Notation and...
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