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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online