mmer 2019 3. Evaluate: M y2 dV where E the solid hemisphere x2 + y2 +z2...
Use spherical coordinates. Evaluate (4 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 16, z ≥ 0. H
4. (9-22 - y2)dV where H is the solid hemisphere ? + 4. Evaluate SS y2 + 22 S 9,220
6. SSSE 23 dV where E is the portion of x2 + y2 + z2 = 9 with z 50 and x > 0
1 point) Use Stoke's Theorem to evaluate (▽ × F)·dS where M is the hemisphere x2 + y2 + z2-16, x > 0, with the normal in the direction of the positive x direction, and F (x6,0,yl) Begin by writing down the "standard" parametrization of ЭМ as a function of the angle θ (denoted by "t" in your answer) a F-dsf(0) de, where f(θ) = The value of the integral is (use "" for theta). 1 point) Use Stoke's Theorem...
Use cylindrical coordinates to evaluate the triple integral ∭E √(x2+y2)dV where E is the solid bounded by the circular paraboloid z = 1-1(x2+y2) and the xy -plane.
5. Evaluate /// (y +z) dV where E is bounded by x = 0, y = 0, x2 + y2 + z2 = 1, and x2 + y2 + 2?" = 9. Use spherical coordinates. Answer must be exact values.
Evaluate the triple integral. 3z dV, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant E
3. Use spherical coordinates: a) Evaluate IILr2 + ข้า dV where E is the solid region inside the sphere 12 + y2 + ~2-16 and above the cone 3r2 + 3y2 b) Find the centroid of the solid hemisphere of radius a, centered at the origin and lying above the xy- plane 3. Use spherical coordinates: a) Evaluate IILr2 + ข้า dV where E is the solid region inside the sphere 12 + y2 + ~2-16 and above the cone...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Evaluate Sed = 25 and E 1 dV, where E lines between the spheres x2 + y2 + x2 x2 + y2 + 22 = 36 in the first octant. x² + y2 + z2