1, Evaluate Jsx2ds where s is the portion of the cylinder 22ヤU-9 lying between z-1 and 22. 2. Let F(, y, z)i+ j + zk....
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...
Could you do number 4 please. Thanks 1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0 < y < 2 oriented by the unit normal pointing out of the cylinder. 5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
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.
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 SS Fods where F= xi + 15 + 2 zk and s is the portion of Surface 2=1-x2 - y2 above the xy plane with upwards orientation the
Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder and the plans JsFinds F(x, y, z) = (x2 + cos(y2))i + (y-e)j + (22 +)k + y2 = 4 +z=2, 2=0.
DIVERGENCE THEOREM Evaluate using the DIVERGENCE theorem Let S be the denote the portion of the graph of the function z-x2 + y2 between the heights 3 and 5. A parameterisation of this surface is r(u, u) = (u cos u, u sin u, t,-) with u E [0, 2π] and u ε [V3, V5]. Let the orientation of this surface have normal with negative z coordinate. Let F-(y,-r,e) be a vector field over R. Let S be the denote...
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...