(1) Use the divergence theorem to evaluate F-S. where F (z, y, 2) = zzi – j+4:k and S is the surface of the region bounded by the paraboloid z = 4- r - y? and the r- y plane.

Q: (b) State the Divergence theorem. Let F = x(y +1}z} . Use the Divergence Theorem to evaluate [[F.îds…

A: given divergence theorem- according to divergence theorem the surface integral of a vector field…

Q: /F-nds, where b) Use Gauss theorem to evaluate F(x, y, z) = (2a²y² + In 2) i – xy° j – tanh(2² + y²)…

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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: Verify: Green's theorem in the plane for f(2x-y³) dx-xydy, where C is the boundary of the region…

A: Given information ∫c2x-y3dx-xydy Here, C is the boundary of the region enclosed by the circle…

Q: (10) Let S be the surface S:= {(x, y, z) E R³: 9x2 + 4y² +2²=1, z 20}. Evaluate the surface integral…

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Q: The function is given piecewise: f(x) = = et 0 tan(x) Is function continuous at x = 0? Explain. if x…

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Q: Calculate F dS if F(x, y, z) = x²yei+ xyj – 2xye k, where S is the surface of the pox bounded by the…

A: Given-F(x,y,z)=x2yezi+xy2j-2xyezk To find- ∬SF.dS ,where S is the surface of the box bounded by the…

Q: b) Given F(x, Y, z) = (x³ + cosh z) i+ (2y³ – 3x²y)j – (x² + 4y²z) k. Use Gauss's theorem to…

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Q: (b) If F(x, y, z) = xzi+3xyj – 2zk, evaluate fF.dS using Gauss's theorem when S is the closed…

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Q: 5. Let F(x,y,z) = (3xy²)i + (xe²)j+ (z³)k. S is the closed surface bounded by the cylinder y? + z? =…

A: 9π/2

Q: 3. Verify Gauss Theorem in evaluate ff F-n ds where F(x, y, z) = 4xzi - y²j+yzk and σ is the surface…

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Q: Calculate ff f(x, y, z) dS For Part of the surface x Js f(x, y, z) ds = S - z³, where 0 ≤ x, y ≤…

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Q: 4. Use Stokes' Theorem to evaluate [ F• dr when z = 4-y F(x, y. 2)= xz° 7+(x+z*)7+ -x |k. Let C is…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 2. Let S be the surface x² + y² = (2-2)², y Evaluate Jl F = (2x+y-xz, -x, -(2 — z)²), choosing a…

A: Using parametrization of the surface S

Q: Take the paraboloid z = 16x² + 16y² for 0 ≤ ≤9 and slice it with the plane y = 0. Let S be the…

A: Given that the paraboloid z=16x2+16y2 for 0≤z≤9 which is slice it with plane y=0 and S be the…

Q: Consider the three points in R³ X1 = (-1,5,8), X2 = (1, 3, 7), X3 = (2,6, 4) and let a = x1 – X2, b…

A: Part (a) When two vectors is perpendicular then their dot product is 0.

Q: Use the Divergence Theorem to evaluate F. dS , where F(r, y, z) = (2x(y - z), x? – y, z) and S is…

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Q: Use Gauss’ theorem to evaluate F.ndS for the given F and o. (b) F(x, y, z) = x³ i+x?yj+xy k, o : the…

A: We will use gauss divergence theorem to find value of given surface integral  If E is a  simple…

Q: Evaluate G if G is a solid in the first octant bounded by the plane y +z = 2 and the surface y = 1–…

A: Use the following formulae, to obtain the solution. a-b2=a2-2ab+b2∫xndx=xn+1n+1+C

Q: Use divergence theorem to evaluate where F(x, y, z) = 3xi + xyj + 2xzk and s is the surface of the…

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Q: Calculate fff, V.F dV where V is a closed space bounded by x = 0, x = 1, y = 0, y = 1, z = 0 z = 1…

A: In general, triple integrals involve the integral with respect to x, y, and z. Similar to partial…

Q: Let F(x, y, z) = -2yi – 3zj – 5xk and C be the circle x? + y? = 9 that forms the boundary of ơ in…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…