Evaluate the following closed surface integral: F.î dA Where F = (xz²i + yz?j + z°k). The surface S: x?+y²+z? = 9 Select one: O a Non of them O c.0 d. 108

Q: 1. Let k be a nonzero constant. Show that the equation of the tangent plane to the surface xyz = k…

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Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

Q: Assume S is the surface x1000+y8000+z1000 = 10¹2 and f = (9+ eyz, x³yz, 3x - 5y - 6 cos(zx)).…

A: Here we use the Divergence theorem for a surface S inclosing a volume V

Q: F = 2yj+z k and S is the surface y? + z? = 4 between x 0 and x = 3 – z. Compute SL.F.ds

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Q: Evaluate SF.nds.... F(x,y,z)=(2z - y)i + xj - 2xk, and S: a sphere of radius 1 centered at the…

A: Evaluate ∬SF⋅n dSF(x,y,z)=(2z−y)i+xj−2xk, andS:a  sphere of radius 1 centered at the origin, and n…

Q: Find a point on the surface x - yz = 11 that is closest to the origin. (a, ± √b, √c), where a ,b= =…

A: We have to find the point on the surface x-yz=11 that is closest to the origin.

Q: Evaluate [[*. F.ds where F=zi+yj+k and S is the upper half the sphere x² + y² + z² = 9 and the disk…

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Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

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Q: Which sets are equal to the set (a, b, c)? {b, b, b, x, x, x, C, C) {b, b, b, b, b, c, c, c, a, a)…

A: What is Set: Set is the language of mathematics. Through set, we can define mathematical expressions…

Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 36. Answer= (x…

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Q: Find the points at which the following surface has horizontal tangent planes: x² + 2y² + z2 – 2x –…

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Q: classify and sketch the following surfaces

A: Sketch of the surface:

Q: Calculate the surface of cylinder x² + y² = 1 that lies between the Z=0 and == x1y+ 2 planes Fax is…

A: Given :Cylinder  x2+y2=1 that lies between the plane z=0 and z=x+y+2. To Find : Surface Area of the…

Q: Consider the surface 4a? – y? + 2z² + 4 = 0. a. Find the value(s) of k such that the cross-section…

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Q: | Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2, 1). Evaluate the…

A: ∫c y2xdx + 4yxdy=? We know that this form of integral is solved by Green theorem: ∮cP dx+Q…

Q: By using stoke's theorem to find its value SS₂ (DXF) .nds where F=(x-2)i + (R+Y2) j-3 and Sis the…

A: The given problem is to find the value of the surface integral of the given vector field over the…

Q: Assume S is a smooth surface parametrized by R(u,v) = (V / za sin y do. Evaluate S Hint: Find the…

A: We use double integral to solve this.

Q: Consider the contour represented in the following figure. The points marked on the figure are А(3,…

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Q: ) The portion of the cylinder x² + z² = 10 between the planes y = −1 and y = 1.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate the surface integral fF- dS where F = (52,-52, 5y) and S is the part of the sphere a² +2+22…

A: Solution