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- Find the surface area of the parametric surface = r(u, v) (u + sin(v), v + sin(u), u-v) where -≤u≤π and T ≤ ≤TT. Enter your answer rounded to 2 decimal places.Find div F and curl F if F(x, y, z) = x²i - 6j+yzk. div F- = 7 x + y curl F zi XFind the area of one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0<=x<= 6, and beneath the curve on the surface ƒ(x, y) = 4 + 3x + 2y
- An integral expression for the area of the surface generated by rotating the curve X =Vv, 1sys8 about the x-axis is S 2 TX°Vdx 1+ 3x* 2 TTX .2 2 TIXV1+ 3x2 dx S, 2 nx*V1+ 9x*dx 3 2 TXV1+9x2 dxFind div F and curl F if F(x, y, z) = x³i - 10j +yzk. div F= curl F=Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).
- Find the area of the portion of the surface x2 - 2z = 0 that lies above the triangle bounded by the lines x = sqrt(3), y = 0, and y = x in the xy-plane.Find the surface area of the part of the surface z = x? + 3y that lies above the triangular region T in the xy-plane with the vertices (0, 0), (1, 0), and (1, 12). Give your answer in 2 decimal places. You have to use the following formula: dz az A (S) = || 1+ dA ду TFind the surface area of the part of the plane 2x + y + z = 4 that lies inside the cylinder x² + y² = 9. Surface Area =
- Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 – cos (v)) sin (u), z = sin (v) at the image of a point (u, v) for –x < v < a and -a < u < a. (Write your solution using the form (*,*,*). Use symbolic notation and fractions where needed.) no = Identify this surface. ellipsoid hyperboloid torus cylinderDetermine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, -1,0).Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the y-axis.