In this exercise we show that the unit cylinder r²+y² = 1 can be covered by a single patch. Let U = {(u, v) | 0 < u² + v² < n²}, and let r = Vu² o(u, v) = (r, y, 2) = (E; tan(r – 7/2) + v². Define rr (a) Show that a² + y² = 1. What is the range of z? (b) Describe how U is deformed to obtain the cylinder. (c) Find the inverse of o and argue that both o and o¬l are smooth.

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A: Find the attachment

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Q: 4. §13.3. Q49. Consider function w=w(x, y, z). (a). Find Ow/dx. (b). Find Ow/ay. (c). Find əw/az. w…

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Q: / (sec. sec u tan u -1) du

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A: Uniform continuity

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Q: et F = t+3 2i-fj+3t°k and G = e'i – 3f j+ e²* & %3D

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Q: Use Green's theorem to evaluate s cy? oy)dx + (y²rlo4") dy where Cis s hoon belbw, N y = 2-x² G,1)

A: The given path contains 4 curves: C1:  from (1, 1)  to  (-1, 1)C2:  from (-1, 1)  to  (-1, -2)C3:…