4. Let the torus T be the image of the map T(u, v) = (x(u, v), y(u, v), z(u, v)) = ((R+r cos v) cos u, (R+r cos v) sin u, r sin v) for all u, v € [0, 2π]. Here T is neither injective nor surjective and R>r> 0. Show that T is a sequentially compact set in R³.

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Q: ii. Use the basic definition of complex integration to evaluate the integral I $, z¹ dz, where the…

A: Step 1: Step 2: Step 3: Step 4:

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Q: Suppose that Find the Jacobian Metrix for map.

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Q: Q4 Evaluate S SR (x + 2y) dA where R is the triangle with the vertices (0, 3).(4, 1) and (2,6) using…

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Q: Let C be the space curve represented by represented by & (+) = [(4-2+, 36-2, 61) a.) Reparametrize R…

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Q: 2. Triangle FGH with verlices F(1,8), G(5, 7), and H(2, 3): y-x F' G' H' - 177

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Q: Let P be the tangent plane to the surface z-2x2+y2 at the point Q=(1,1,3). Which of the following…

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Q: (b) Every continuous map S? →T² is homotopic to the constant map.

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Q: 2. Given f (x, y) = x + 2y, find F(x, y) =Vf and sketch it along with the contour map of f.

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