(1 point) Verify the Divergence Theorem for the vector field and region: F-(2x, 82.9y〉 and the r...
(1 point) Verify that the Divergence Theorem is true for the vector field F = 3x´i + 3xyj + 2zk and the region E the solid bounded by the paraboloid z = 9 - x2 - y2 and the xy-plane. To verify the Divergence Theorem we will compute the expression on each side. First compute div F dV JE div F= Waive av = f II Σ dz dy dx where zi = MM y1 = y2 = MM мм...
(1 point) Verify that the Divergence Theorem is true for the vector field F-3z2ì + 3z30-22k and the region E the solid bounded by the paraboloid z = 16 z2 y2 and the zy-plane To verify the Divergence Theorem we will compute the expression on each side. First compute div F dV div F div F dV- dz dy dr where div F dV- Now compute F dS Consider S- PU Dwhere P is the paraboloid and D is the...
Problem (10 marks) Verify the Divergence Theorem for the vector field F(x, y, z) = (y,1,-) on the region E bounded by the planes y + : = 2 := 0 and the cylinder r +y = 1. Surface Integral: 6 marks) Triple Integral: (4 marks)
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
Q.7, as question above 7. Verify the divergence theorem for F(x, y,z) - by the sphere x2 + y2 + Z2-4. 4xöx +yy +4zőz and V is the region bounded (15 points) 7. Verify the divergence theorem for F(x, y,z) - by the sphere x2 + y2 + Z2-4. 4xöx +yy +4zőz and V is the region bounded (15 points)
Use the divergence theorem to find the outward flux(F n) dS of the given vector field F y21+ xz3j + (z-1)2k; D the region bounded by the cylinder x2 + y2-36 and the planes z-1,2 F 1, Z 9 eBook
a) What is the Surface Integral b) What is the Triple Integral Verify the Divergence Theorem for the vector field F(x, y, z) = (y,1,22) on the region E bounded by the planes y + 2 = 2, 2= 0 and the cylinder r2 + y2 = 1.
Problem #4: F.ndS Use the divergence theorem find the outward flux of the field to vector e+7 cosxj +y? and x2 + y2 V 49 an (3y + 8z) i 2 2 k, where S is the surface of the region bounded by the F graphs of z Vx V + symbolically, Enter your answer (sqrt(2)-1)*(686/3*pi) as in these examples Problem #4 686 JT 3 Submit Problem # 4 for Grading Just Save Attempt #3 Problem #4 Attempt #1 Attempt...
Use the divergence theorem to find the outward flux F:n) ds of the given vector field F. JJS F = y2i + xz?j + (z 1)2k; D the region bounded by the cylinder x2 + y2 = 36 and the planes z = 1, z = 7 eBook
vector Problem #5: Use the divergence theorem to find the outward fly SfF:nds of the field F = tan-1(10y + 3z) i + e sxj + 1x2 + y2 + z2 k, where S is the surface of the region bounded by the graphs of z = Vx2 + y2 and x2 + y2 + z2 = 49. ,z2 + 3 cos x + Problem #5: Enter your answer symbolically, as in these examples