Use the Divergence Theorem to evaluate F. dS where F = (2²a +y?. + tan (2), a?z – 1 2, and S is the top half of the sphere ? +y? + 22 = 1. Hint: S is not a closed surface. First compute integrals over S, and S2, where S, is the disk 2 + y?< 1, z = 0 oriented downward and S2 = SUS F. dS1 I dy da = F. dS1 = Σ F. dS, = 2 dz dy da where Σ Y1 = 21 = Σ Σ 2 = Σ 22 = Σ F. dS2 = Σ F. dS = Σ M M

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Q: 1. Use the Divergence Theorem to evaluate /| F.dš where F.dSv F = yx? i+ (xy? - 324) j+ (x³ + y?) k…

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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: Use the Divergence Theorem to evaluate [, F• dS, where F(x, y, z) = z²x i + (y + tanz)j + (x²z +…

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Q: Use the Divergence Theorem to find the flux of F accross S; that is calculate LlF• nds where F(x, y,…

A: Topic : vector calculus

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Q: Verify the formula F.ndS = div F dV G in the Divergence Theorem by evaluating the surface integral…

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Q: Evaluate the following contour integral f(z)dz , using the z2-1 parametric representation for C,…

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A: Given data:

Q: Let S:x+z? = 16,0sys3 be the surface of a closed cylinder bounding a volume T.F=[z?, y, x²]. Use the…

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Q: Use the Divergence Theorem to find F- ndS, where F = (y°z,x²z,z') and the surface S is the sphere x…

A: See the details solution below

Q: Use the Divergence Theorem to evaluate F. dS where S is the sphere r² + y² + z² = 9 and F = (3r, 2y,…

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Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

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A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Use the Divergence Theorem to determine the value of f f, F•dS where F (x, y, z) = (3x – x² )i+…

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Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

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Q: Let T be the quarter sphere solid that is inside x°+ 4?+Z* = | for x20. Let S be the Closed surface…

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Q: Evaluate both sides of divergence theorem for A= pa, + pcos(0)a , + zaz through the closed surface…

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Q: Let F(x, y, 2) = 32?ai+ (y³ + tan(z))j+ (3x²z- 4y?)k. Use the Divergence Theorem to evaluate fs F dS…

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