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#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...
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...
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...
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...
(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 + yj + zk over the quarter cylinder S given by x2 + y2 -1, 0 3x s 1,0
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F= <2y, y, z2> and S the closed surface formed by the paraboloid z = x2 + y2 and the disk x2 + y2 ≤ 4 at z = 4. Use divergence theorem to solve one way, and use SSs F * N ds to solve the other way. (This is a Calculus 3 problem.) * 36.3. Compute in two ways the fux integral ф...
Evaluate ∫∫ (x2i+ xyj+ zk) ∙ ndA over the closed surface bounded by the paraboloid S: z = 4 − x2−y2, on sides, and the bottom plane z = 0 (a) directly, (b) by the divergence theorem.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane. 6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
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...
3. (5 points) Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) - 3ry? i + xe'j + 23k across the surface of the solid bounded by the cylinder y2 + z-1 and the planes z =-1 and x = 2. 3. (5 points) Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) - 3ry? i + xe'j + 23k across the surface of the solid...
2. Calculate the flux of the vector field F (2ry,-y2 + 3y, 1) through the surface with boundary Soriented with the outward unit normal in the figure below. Assume the volume of the solid E which lies inside the surface S and above the ry plane is 2π. Follow the following steps. [Warning: The problem is very similar to the one in PS11 but they are not the same. We can not apply the Divergence Theorem to S since it...