Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=x³i-3x²yj+7xzk 2 D: The region cut from the first octant by the sphere x² + y² + z² = 4

Q: Find the equation of tangent plane to this surface at the point where x :1 and y = -1.

A: Given surface is z=f(x,y)=sin(π (3x+2y)) +x2y2 Equation of tangent plane is given by,…

Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: Use the divergence theorem to calculate ff, FdS where F = x²yi - xy² j - xyz k. S is the surface of…

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Q: Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin,…

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Q: Let D be the unit disk D = {(x, y) | x² + y² ≤ π }. Calculate ə Ə ₁ ( [xsin (2² + y²³)] - [3² sin(x²…

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Q: Use Divergence theorem to evaluate ff, F. dA, where S is the surface of the region bounded by the…

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Q: c) Calculate (x+y + 2) dV, where E is the region bounded by r2 + y +z s 25 and above the E xy-plane.

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Q: The region W lies between the spheres x² + y² + z² = 4 and x² + y² + z² = 16 and within the cone z =…

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Q: The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2i -…

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Q: Compute the surface integral s F-ndo. F = xyi - x¹j+ (x+z)k. The surface is the top of the plane 2x…

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Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: Let F = 2x3i + 2y3j + 2z3k and let S be the surface consisting of the hemisphere x2 + y2 + z2 = 1, z…

A: Given, F=2x3i+2y3j+2z3k and  S be the surface consisting of the hemisphere x2+y2+z2=1, z≥0 and the…

Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

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Q: Let S be the solid obtained by rotating the region bounded by C1: y = x2 − 6x + 9 = (x − 3)2 and C2:…

A: The given curves are y=x-32, and y=x+3. To Sketch: The region bounded by the above curves and which…

Q: D) Evaluate f (r² + y²) dady where D is the disk z² + y² ≤ 4. Usc polar coordinates. (Ans: 647/5) E)…

A: To solve the following

Q: Find the points on the sphere with center at the point P-(3,3,3) of radius 3 where the function f(x,…

A: Using Lagrange multiply method

Q: Find a parametric representation for the surface S, where S is the part of the cylinder x2+y2 = 4…

A: A surface S where S is the part of cylinder x2+y2=4 which lies between z=-2 and y+z=2. To Find:…

Q: Let W be the region between the sphere of radius 8 and the sphere of radius 7, both centered at the…

A: be the region between the spheres of radius 8 and 7 both centered at origin.And We have to find…

Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: Let S be the bounded portion of the paraboloid x² + y² = 8z which is cut off by the plane z = 4.…

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