IF F= 3yI - Xy I+ 9ZK and s is the Surface of the Pasabolied 2X =x2 fy Bounded By Evaluate %3D I=2 ff(VXF). ds ising stoks theorem,

Q: Calculate :/ F. ds, where F (x, y, z) = (-6x³ + 2yz)i + (-6y³ + sin¯¹ (3xz)) j+ (2z+cos (3x²y²)) k…

A: Given F(x,y,z)=-6x3+2yzi^+-6y3+sin-13xzj^+2z+cos3x2y2k^ and S is the outward-oriented surface of the…

Q: C:1-1,4), (1,2) (-レ-1),(ル-) the boundary of the rectonale that accepts points as a corner…

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Q: 3. Let C be the circle x + y = 16 and let S be any surface above the xy-plane with C as its…

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Q: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

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Q: Sketch the surface 1≤z≤ √9-x² - y² 1≤z≤√9-x² - y² and_x² + y² ≤1

A: Given is the surface surface 1≤z≤9-x2-y2 and x2+y2≤1 The objective is to sketch this surface.…

Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

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Q: ) Every continuous map RP2 → S² is homotopic to the constant map.

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Q: [F•dš where F=xỉ - yj+(x+ y+z)k

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Q: Q2: f(x. y)- x/y over the region in the first quad- rant bounded by the lines y x,y 2x,x 1,x-2

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Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

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Q: Evaluate exp{}dA where R is the region in the ry-plane bounded by the trapezoid with vertices (0,…

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Q: (27) Find the surface area of the part of the sphere x² + y² + above the xy-plane and it is…

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Q: Evaluate e fy³dz — 2³dy, where C' is the boundary of the region between the circles æ² + y² = 4 and…

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Q: Evaluate yºda – x³dy, where C' is the boundary of the region between the circles œ² + 1² = 1 and x²…

A: The given problem is to evaluate the given line integral over the given path C where C is boundary…

Q: Please sketch the following (do it by hand and not software): a) The space curve defined by r(t) =…

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Q: Sketch the surface 1≤z≤√√9-x²-y²_and_x² + y² ≤

A: Solution is below

Q: Let M⊂R ^ 3 be a surface and f be a diff.bilir function on this surface. Show that if Q is this…

A: Given: Let M⊂R3be a surface and let f be a differentiable function on this surface. If Q is a 1-1…

Q: Eind equatons of the following x²-2y²+2²+ yz =20, [4,6-3) W the tangent plane 6 the normal line to…

A: Solution: f(x,y,z)=x2-2y2+z2+yz-20

Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: Exercise 5. Compute F F.NdS where F(x, y, z) surface of the plane x + 2y + z = 6 in the first…

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Q: d(fv) = df ^ ¢v + fdý %3D

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