A2. Use the divergence theorem to evaluate ff, FdS where F = on the surface that consists of three surfaces 2² + y² = 1,0 ≤ ≤ 1 on the sides, z = 0 at the bottom. ryi + = 4-3r² - 3y², 1 ≤ y²j + zk and ≤ 4, on top

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: Does the Divergence Theorem apply to surfaces that are not closed?

A: By Stokes' theorem:

Q: b such that the surf 4x2y + z3 = 4 cut -1 ?). %3D

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Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

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A: v1=1-32, v2=-39-6 and v3=5-7h

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: Solve: 2 0 -1 0 2 -6 1 -2 -3 -2 0 1 -5

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A: Simplify the integral:  ∫Ωr→r3∇→r4-R4r5+7r3+2dτ=∫Ωrr3r^r^ddrr4-R4r5+7r3+2r2sinθdrdθdϕ…

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

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A: We know that two planes are parallel if their normal vector are parallel. That is their, gradient…

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A: Given: f(x)=x+sin x  (0≤x≤2π)To find the critical points, endpoints, local/global maxima and minima…

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A: Sol:-] To derive a cubic spline with natural boundary condition, we need to find the cubic…

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Q: 9) of which of the following is the groph X² y = = A) 24 B) c) D) 24 ²4

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A: The two given planes are x-y+z=0 and x+y+2z=0.

Q: - {z,y, 2)| 2 2= > 0} //| dpdød0 set Consider the 3D domain W = Calculate | a2 + y? + z² d(x, y, z)…

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Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: 44. Use Gauss's Theorem to evaluate fF-d$ if F=x³i+y³i+z³k where S is the closed surface of the…

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Q: d(fv) = df ^ ¢v + fdý %3D

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Q: Show that 7(u, v)= (²-²,2ue) maps the triangle-((u, v):05≤SS 3) to the domain D bounded by z = 0, y…

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