(1 point) Compute the flux of F xi + yj + zk over the quarter cylinder S given by x2 + y2 -1, 0 3x s 1,0 <y<1,0 3z< 1, oriented outward flux = (1 point) Compute the flux of F xi + y...
(1 point) Compute the flux of F = 4xi + 4y] + zk over the quarter cylinder S given by x2 + y2 = 9,0 < x < 3,0 <y <3,0 < z <3, oriented outward. flux =
#4 please 3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) -xi yj+3 k S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y 0 and x y 2 Evaluate the surface integral F dS for the given vector field F and the oriented surface...
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π 9. Let Q be the solid bounded by the cylinder x2 + y2...
can you solve this vector problems? Find the outward flux of the vector field F(x, y, z) = (xi + yj + zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2 = 1. 6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1 6. (12 pts.) Find the outward flux of the vector...
Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For dlosed surfaces, use the positive (outward) orientation F(x, y, 2) _ yj-zk, sconsists ofthe paraboloid γ_x2 +22, O sys1, and the disk x2 +22 s 1.7-1. Need Help? to Tter Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the...
zi+yj + zk 3. Given the vector field in space F(x, y, z) or more conveniently, (x2 + y2 + 22)3/2 f where r = ci + yj + zk and r= |||| = V2 + y2 + z2 (instead of p) 1 F(r) = r2 (a) [10 pts] Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral lle F.NDS where S is the unit sphere x2 + y2 + z2 = 1...
Find the flux of the vector field F = xi + e j + zk through the surface S given by that portion of the plane 7x + y + 3z = 5 in the first octant, oriented upward.
Let F(x, y, z) = xi + yj + zk and S be the surface defined by z = 9 – 22 - y2 and 2 > 0. Evaluate SsFinds, where n is the upward unit normal vector.