3.) Verify the conclusion of Stokes' Theorem given F(x,y,z)=(x-y,y-z,z–x) where S is the surface cut from the plane with equation x+ y+z=3 by the cylinder x +y =1. Assume that the boundary of S is oriented counterclockwise when seen from above.

Q: Sketch and describe, in your own words, the surface S parametrized as follows: r(u, v) = (3 cos v,…

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Q: Use properties of the linear transformation T(x, y) = (3x − 2y, x + y) to determine if the matrix…

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Q: Given the surface z = In(-2x² + 5y² – xy). Find the directional derivative of the function f at…

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Q: Let z = g(z, y) = f(3 cos(ry), y + e") provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) = 3. i)…

A: Let z=gx,y=f3cosxy, y+exy f3,7=4, f13,7=2, f23,7=3

Q: 2) Using Stokes theorem, evaluate pvdr where v= 2y'i– 2x° j+÷k_and the C is the curve of C…

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Q: 6) Use Stokes' Theorem and Theorem 10 in section 16.7 to find § F · dř. F(x, y, z) = (2y, xz, x + y…

A: .C is oriented counterclockwise, and it is the intersection of the plane  and the cylinder .To Find:…

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

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Q: Ic F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 5zj + 7yk,…

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