# What is the value of s 1 u v cosh u 2 sinh u v f

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Unformatted text preview: 2 Φ : [0, 2π ] × [1, 2] → R3 , Φ (u, v ) = (cosh u, 2 sinh u, v ) Φ : [0, 2π ] × [1, 2] → R3 , Φ (u, v ) = (cos u, 2 sin u, v ) Φ : [0, 2π ] × [1, 2] → R3 , 10. What is the value of S 1 Φ (u, v ) = cosh u, 2 sinh u, v F · dS ? where F (x, y, z ) = (xz, yz, x2 − 24yz )? −6π 6π 2π −2π For questions 11-12, let C be the oriented tilted ellipse positively parametrized by c (θ) = y (3 cos θ + sin θ , cos θ + 7 sin θ), θ ∈ [0, 2π ]. Let F (x, y ) = (P, Q) where P = − x2 +y2 and x Q = x 2 +y 2 . 11. Which of the following is equal to x +y x 2 +y 2 ∂Q ∂x − ∂P ∂y on R2 \ {0}? −2x2 +2y 2 (x2 +y 2 )2 x −y (x2 +y 2 )2 0 12. What is the value of C F · ds? 0 π −2π 2π Hint: Introduce a closed curve inside the ellipse and use the result in question 11. Be careful with how you orient the curves. Page 2...
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## This note was uploaded on 02/12/2014 for the course MATH 3010 taught by Professor Magpantay during the Fall '13 term at York University.

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