Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axi...
Question 1. Let C be the intersection of the plane -2r +5y with the cylinder r2+y2= 1 Find a parameterization for the curve C, oriented so that C is traversed counterclockwise when viewed from the positive z-axis. Select bounds for the parameterization so the curve is traversed exactly once. Let F = (y,z,-a). Compute F ds. . C
Question 1. Let C be the intersection of the plane -2r +5y with the cylinder r2+y2= 1 Find a parameterization for the...
Use Stokes' Theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from above. F(x, y, z) - xy + 27 + 6yk, C is the curve of intersection of the plane X + 2-1 and the cylinder + 9.
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal.
F-dS where S is the cylinder x? +-2, 0 s y
Use Stokes' theorem to find the work done by the force field F(z, y, z)-<-r, z, y > along the positively oriented curve of intersection of the cylinder 2+y 1 and the plane 3x +z 4 9.
Use Stokes' theorem to find the work done by the force field F(z, y, z)- along the positively oriented curve of intersection of the cylinder 2+y 1 and the plane 3x +z 4 9.
Evaluate z) ds, where S is the intersection of the plane z=4-y with the solid cylinder x2 + y2 33. 8. 127211 ob.8V21 C. None of these O d. 4√3 a e. 1231
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); + (x+y); + (4y2Z) K and the curve C defined by the intersection Counter clockwise as viewed from above. Evaluate the Work- SF. dr done by F along in the following ways (a) Directly, using parametrization of C (b) Using stakes theorem
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes' Theorem. , where S is the up
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y...
Evaluate the Surface Integral, double integral F*ds, where F = [(e^x)cos(yz), (x^2)y, (z^2)(e^2x)] and S is a part of the cylinder 4y^2 + z^2 =4 that lies above the xy plane and between x=0 and x=2 with upward orientation (oriented in the direction of the positive z-axis). ASAP PLEASE
11. F (z, y, z)-(2c3 + уз) i + (уз + z3) j + 3уг z k, S is the surface of the solid bounded by the paraboloid z 1-2 -v2 and the zy-plane Answer 11. F (z, y, z)-(2c3 + уз) i + (уз + z3) j + 3уг z k, S is the surface of the solid bounded by the paraboloid z 1-2 -v2 and the zy-plane Answer
11. F (z, y, z)-(2c3 + уз) i + (уз...
Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = zeli + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 4, y 2 0, oriented in the direction of the positive y-axis.