Use the divergence theorem to evaluate te ff. F. Is by paraboloid y = x² + 22-2, cylinder x² +22=1, and plane x + y = 2, and S is oriented outward. I 9x 2 F-ds, where F(x, y, z) = xi + yj + zk and S is the boundary of the solid enclosed

Q: 20. A O e'dr C e'dr Le dr. D

A:

Q: A.W:-Evalwte the intagral Ic2 - i) dz where c is; line OThe straight 9= 2x jeining Aceso) to BC1,) A…

A:

Q: Find the surface area of the portion of the plane z=6-3x-3y which lies in the 1st octant I)2sqrt18…

A:

Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: sin(7y), 8x2+7x°cos(7y)). vative servative n of the parabola y=x2-16 from (4,0) to (-4,0). Which of…

A: We have to choose the option

Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: Find the center C and the radius r of the sphere S :x2 +y? + z2 - 2x 4y + 4z = 16 O C (2, 4, -4) and…

A:

Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…

A:

Q: Consider the planes P₁: 3x+y-2zm 7 and P₂ : x+2y+z=4. Give a parametrization for the line of…

A:

Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

A:

Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

A:

Q: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

A: Let the given square be OABC which is positively oriented.

Q: Q: If the point (x, y) is equi distant from the points (a+ b,b-a) and (a-b,b+a). Prove that bx = ay.

A: Use given conditions to prove bx=ay

Q: 2 The values of a and b such that the surfaces ax - byz = (a + 2)x and 4x2y + z3 = 4 cut…

A:

Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

A:

Q: V=R Prooflthat Nisavectors sPoe

A: Given that V = ℝ+ Operations + and · defined as, x + y = xy rx = xr, where x,y ∈V; r ∈F To prove: V…

Q: equation of the line. -y+22-0 passing through cting line e:x=2+t,y=st,

A:

Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

A:

Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

A:

Q: Which of the following planes are not parallel to the plane -x+ 3y + z = 3? Select all that apply. O…

A: Our objective is to find the required plane.

Q: Find the intersection of the plane x - X = y = - 4y - 5z = -137 and the line r(t) = (5, −5, −4)t +…

A:

Q: es v3x + z – 5 = 0 and 2x + 2/3z + 10 = 0. ond

A: