Use Gauss' Divergent Theorem to calculate F. dS. where F = (sin(y?) + a)i + ey?j – 2e*+cos² (au)k and S it's the border of the cube 1 < < 2,0 < y < 1 and –1 < z < 0. consider the normal field pointing out of the cube.

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A: Solution

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Q: Convert 60013g to decimal. Show your work.

A: See the detailed solution below.

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A: To evaluate, ∮1zdz over the unit circle counter-clockwise

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Q: Find the line integral of the field F = over the portion of the ellipse * + y = 1 lying in the first…

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Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

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Q: Find div F and curl F if F(x, y, z) = 4y°z'i – 11x"2°j – 4xy°k. div F= curl F=

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Q: Compute the following definite integral of a vector-valued function: Cos t i- tj + te’k ) dt sint +1

A: Please refer the attached image for complete solution.

Q: late the F= (x - y) i - (x 2 + y 2) j; C is curve from (4, 0) to (-4, 0) on the upper half of the…

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Q: ) Verify Stokes' Theorem for the hemisphere S : x²+y²+z² = 9, z > 0, %3D its bounding circle C: 1?…

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Q: EX2 : Find Divergence and Curl of the field function f j = In (x? + y?)i – 2z -tan + (5z + e' cos…

A: givenf→=ln(x2+y2)i-(2zxtan-1yx)j+(5z3+eycosz)kdefinition of Divergence…

Q: L4. (a) (b) A function f is given by f(x, y, z) = 4x³yz + (3xy²)-¹ + If x = 1, y = -²±², z=-1t 23…

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Q: .) Find the work done by field F = (-y,-x) along curve C: counter clockwise along semicircle y = v4…

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Q: (b) The straight line (0, 0, 0) to (2, 1, 3) 3.10 A vector field is represented by F = p°a, + zas +…

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Q: divargen.ce. and.cur..

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Q: 7. You must explain your reasoning. Consider the following radial vector field F: (a) Is Fa…

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