# Chapter 13

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

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online