Chapter 13

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Unformatted text preview: escriptions? 3–8 |||| Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point. 3. 2, 5. 3, 0, 4, 1 6 4. 1, 3 6. 1, , e 2, 2 5E-13(pp 878-883) 1/18/06 11:46 AM Page 879 S ECTION 13.7 CYLINDRICAL AND SPHERICAL COORDINATES 7. 4, ■ ■ 9–12 ■ ( ■ ■ ■ ■ ■ 10. 3, 3, 1, 4 s3, 2) 1, ■ ■ 6, 6 ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ 13–18 |||| Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point. 13. 1, 0, 0 6, 6 16. 5, , 17. 2, 3, 4 18. 2, ■ 19–22 ■ ■ ■ ■ ■ 19. (1, s3, 2 s3 ) 21. 0, ■ 1, ■ 23–26 22. ■ ■ ■ ■ ( ■ ■ ■ ■ ■ 6, s3 ) 25. (s3, ■ ■ ■ ■ ■ ■ ■ 2 2 z 2 2 2 1 y z 56. z ■ ■ ■ x ■ 2 2 2z 0 y2 ■ ■ ■ ■ Sketch the solid described by the given inequalities. r2 2 2, 2, z r 0 2, 3, 2 0 2 2 2, 0 3, ■ 2 ■ ■ 6, sec 0 2 ■ ■ ■ ■ ■ ■ ■ ■ outer radius 7 cm. Write inequalities that describe the shell in an appropriate coordinate system. Explain how you have positioned the coordinate system with respect to the shell. 8, 3 ■ z2 63. A cylindrical shell is 20 cm long, with inner radius 6 cm and 4, s2 ) ■ y2 54. y 4 ■ z 59. ■ 2 2y 62. 0 ■ 26. 4, ■ 2z ■ |||| 2 61. 1, 1, s6 ) ■ 24. (s6, 1) 2, ■ y 2 60. 2 Change from cylindrical to spherical coordinates. 23. (1, y 58. 0 3 20. (0, s3, 1) 1 ■ |||| ■ 4, 50. x 2 52. x 2 ■ 57. r 2 Change from rectangular to spherical coordinates. |||| 55. x 2 57–62 15. 1, ■ 2 ■ 14. 3, 0, y2 3 53. x 12. 3, 4, 5 ■ x2 51. x 2 879 49–56 |||| Write the equation (a) in cylindrical coordinates and (b) in spherical coordinates. 49. z Change from rectangular to cylindrical coordinates. |||| 9. 1, 11. 8. 5, 3, 5 ❙❙❙❙ ■ ■ ■ 64. (a) Find inequalities that describe a hollow ball with diameter 27–30 Change from spherical to cylindrical coordinates. |||| 28. (2 s2, 3 29. 8, ■ 6, ■ 2 ■ ■ ■ ■ 2, 30. 4, 27. 2, 0, 0 30 c...
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This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas at Austin.

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