32 major axis 2 8 minor axis 2 4 c2 a2 b2 c2 foci 0 2

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Unformatted text preview: gular 7 6 7 6 23 2 5, 0, 2 , rectangular Section 10.7 7. 0, 5, 1 , rectangular r 0 2 Cylindrical and Spherical Coordinates 11. 2, r 2, 22 arctan 1 4 , rectangular 2 2 253 9. 1, 5 r 3, 4 , rectangular 1 2 5 5 0 2 3 2 2 22 4 arctan z 1 2 z arctan 3 4 3 z 4 2 2, 4 , 5, , 1 , cylindrical 2 2, , 4 , cylindrical 3 15. y r sin sin r x2 r cos r cos2 sec tan 2 4 , cylindrical 13. x2 y2 r2 z2 z 2 10 rectangular equation 10 cylindrical equation rectangular equation cylindrical equation 17. r x2 x2 2 y2 y2 4 z 3 2 −3 19. 2 tan 1 3 x x y 2 −2 −3 3 z 6 6 y x 3y 3y 0 y x x 2 1 2 y −2 2 1 −2 21. r r2 x2 x2 x2 2 sin 2r sin y2 y2 y z 2y 2y 1 2 0 1 2 1 −2 2 x −1 −2 y x 3 2 1 2 23. r 2 x 2 z2 y2 4 z2 4 −2 x 2 1 −1 2 1 z 25. 4, 0, 0 , rectangular 42 arctan 0 −2 2 y 02 0 2 02 4 arccos 0 4, 0, 2 , spherical 27. 2, 2 3, 4 , rectangular 2 arctan arccos 4 2, 1 2 4 2 29. 42 42 3, 1, 2 3 , rectangular 3 1 12 6 6 4 1 arctan 3 3 arccos 2 23 3 2 2 3 2 , , spherical 34 4, , , spherical 66 254 Chapter 10 Vectors and the Geometry of Space 3 5, , , spherical 44 x y z 5 sin 5 sin 5 cos 55 ,, 22 39. x2 2 31. x y z 4, , , spherical 64 4 sin 4 sin 4 cos 6, 4 4 4 cos sin 6 6 22 6 2 33. x y z 12, 4 , 0 , spherical 0 0 35. 12 sin 0 cos 12 sin 0 sin 12 cos 0 4 4 3 cos 4 4 3 sin 4 4 3 4 5 2 5 2 52 2 12 0, 0, 12 , rectangular 2, 2 2 , rectangular 52 , rectangular 2 37. (a) Programs will vary. (b) x, y, z ,, 41. x2 2 2 y2 36 z2 36 rectangular equation spherical equation 3, 4, 2 0.927, 1.190 43. 9 x 5.385, y2 sin2 sin2 9 rectangular equation cos2 9 3 2 2 2 z sin2 sin2 y2 z2 4 −2 x 2 2 1 −2 1 −1 2 y sin 3 csc spherical equation 45. cos 3 2 3 4 3x 2 z 6 2 47. x2 4 cos y2 y2 y 2 z x2 x2 z2 x2 3y 2 y2 z2 z y2 z y2 z2 0 z2 z2 z 4z 2 2 z2 z2 x 2 −2 −1 1 −1 1 2 y −1 −2 x2 x2 x2 0 4 4z y2 5 z2 4 3 2 −2 x 3 2 1 2 3 −3 y 49. sin x2 x2 csc 1 y2 y2 z 2 1 −2 x 2 1 −1 −2 1 2 −2 y 51. 1 1 4, , 0 , cylindrical 4 42 4 arccos 0 2 02 4 53. 4, , 4 , cylindrical 2 42 2 arccos 4 42 4 42 42 4, , , spherical 42 4 2, , , spherical 24 Section 10.7 57. 12, , 5 , cylindrical 122 52 13 Cylindrical and Spherical Coordinates 255 55. 4, 6 , 6 , cylindrical 42 62 2 13 59....
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This note was uploaded on 05/18/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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