How to solve it? Let F =< -2, x, y2 >. Find S Ss curlF.nds, where...
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
using this formula 2. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over the paraboloid z=1 – x2 - y2, z > 0. SA errom bove de SS (-P (- Puerto Q + R) dA dy
pls show the work clearly 9. Find | V x F ñds where F =< 22,4x, 3y >, the surface S is the cap of the sphere S x2 + y2 + z2 = 169 above xy-plane and the boundary curve C is the boundary of S.
Let f(x, y) = x2 – yż and D= {(2,y) : x2 + y2 < 4}. Let m and M be the absolute minimum and maximum values of f over D respectively. What is m - M?
2. Let I be the surface of the cone z = V x2 + y2 (without the top) between planes z = 0 and z = 2. Let F =< x,y,z2 >. Calculate the upward directed flux SS FdS (a) Using the Divergence Theorem. (10 points) (b) Without using the Divergence Theorem. (20 points)
Let f(x)= kx + 5 x-1 for x<2 for x > 2 . Find the value of k for which f(x) is continuous at x=2.
Let F(x, y, z) = 4i – 3j + 5k and S be the surface defined by z = x2 + y2 and x2 + y2 < 4. Evaluate SJ, F.nds, where n is the upward unit normal vector.
Let F = < - yz, 12, my >. Use Stokes' Theorem to evaluate || curiF . d5, where S is the part of the paraboloid z = 13 – 2? - y that lies above the plane z = 12, oriented upwards Preview Get help: Video License Points possible: 1 This is attempt 1 of 3. Submit
Let F = < x-eyz, xexx, z?exy >. Use Stokes' Theorem to evaluate slice curlĒ ds, where S is the hemisphere x2 + y2 + z2 = 1, 2 > 0, oriented upwards.
1. Let F(x, y, z) = (-y + ,2-2,2-y), and let S be the surface of the paraboloid 2 = 9-32 - v2 for 2 > 0. oriented by an upward pointing normal vector. Note that the boundary of S is C, the circle of radius 3 in the xy-plane. Verify Stokes' Theorem by computing both sides of the equality: (a) (1 Credit) || (D x F). ds (b) (1 Credit) $F. dr