Question

number 6.

to udestyoRe phenomena ren is the Key to understanding these ty ercises 1. Let S be the portion of the plane 2x + 3y+ z Let S be the portion of the surface z-x2 +y2 lyin between the points (0, 0, 0). (2, 0, 4). (0, 2, 4), and (2, 2, 8). Find parameterizations for both the surface and its boundary aS. Be sure that their respective orientations are compatible with Stokes theorem. 5 lying 2. between the points (-1, 1, 4). (2, 1.-2), (2, 3, -8), and (-1,3, 2). Find parameterizations for both the surface S and its boundary aS. Be sure that their respective orientations are compatible with Stokes theorem. Exercises 3 to 6, verify Stokes theorem for the given surface S and boundary aS, and vector fields F 6. Sas in (3), and F +j +k (oriented as a graph) 7. Let C be the closed. piecewise smooth curve formed b traveling in straight lines between the points (0, 0, 0), (2, 0. 4), (3, 2, 6), (1. 2, 2), and back to the origin, in that order. (Thus the surface S lying interior to Cis contained in the plane z= 2x.) Use Stokes' theorem to evaluate the integral: as={(x, y): x2 + y2=1} F xi+i+ k 4. Sas in (1), and F yii+ xk (oriented as a graph) (zcos x) dx+(yz) dy + (vz) dz 2We saw an instance of the law of conservation of angular momentum in Section 4.1 ite fallacious argument, showing that a cat cannotturn itself over(!). is this: "Accept from physics that angular momentum is the moment of inertia times angular velocity Imoments of inertia are discussed in Section 6.3]. But the angular momentum of the cat is zero, so the angular velocity

Answer 1

" Here n^cap = (x, y, z)/1 and F^rightarrow = z^2 i^cap + xj^cap + y^2 k^cap nabla^bar times F^bar =