Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

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11, p = 1, 0 = φ < π/6, 0 = 0 < π 12. 1 < p = 2, 13. 2 < p = 4, 14. p ≤ 2, p≤ csc X 15. A solid lies above the cone z = √√√x² + y² and below the sphere x² + y² + z² = z. Write a description of the solid in terms of inequalities involving spherical coordinates. 16. (a) Find inequalities that describe a hollow ball with diameter 30 cm and thickness 0.5 cm. Explain how you have posi- tioned the coordinate system that you have chosen. (b) Suppose the ball is cut in half. Write inequalities that describe one of the halves. 17-18 Sketch the solid whose volume is given by the integral and evaluate the integral. 17. π/2 < φ = π 0 = φ = π/3, 0 = 0 < π gag on i T/6 3 21 0 2 ²p² sin & dp de dó π/4 27 seco 2 18. S/2 p² sin & dp dº do 19-20 Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over the solid shown. 19. 3 ΖΑ ZAU mom stave ruba y sdg 20. XX 2 ZA 21-34 Use spherical coordinates. 21. Evaluate fff (x² + y² + z²)²dV, where B is the ball with center the origin and radius 5. S the cones. 28. Find the a its center. 29. (a) Find t Ф= 1 (b) Find t 30. Find the v x² + y² + z = √x² 31. (a) Find t stant c (b) Find t 32. Let H be a point is pr (a) Find t (b) Find t (c) Find t 33. (a) Find t radius (b) Find t diame 34. Find the m radius a if distance fr 35-40 Use cy more appropria 35. Find the v cone z = 36. Find the v radius a by angle of T 37. A solid cy height h. (a) Find t (b) Find th of its
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Transcribed Image Text:11, p = 1, 0 = φ < π/6, 0 = 0 < π 12. 1 < p = 2, 13. 2 < p = 4, 14. p ≤ 2, p≤ csc X 15. A solid lies above the cone z = √√√x² + y² and below the sphere x² + y² + z² = z. Write a description of the solid in terms of inequalities involving spherical coordinates. 16. (a) Find inequalities that describe a hollow ball with diameter 30 cm and thickness 0.5 cm. Explain how you have posi- tioned the coordinate system that you have chosen. (b) Suppose the ball is cut in half. Write inequalities that describe one of the halves. 17-18 Sketch the solid whose volume is given by the integral and evaluate the integral. 17. π/2 < φ = π 0 = φ = π/3, 0 = 0 < π gag on i T/6 3 21 0 2 ²p² sin & dp de dó π/4 27 seco 2 18. S/2 p² sin & dp dº do 19-20 Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over the solid shown. 19. 3 ΖΑ ZAU mom stave ruba y sdg 20. XX 2 ZA 21-34 Use spherical coordinates. 21. Evaluate fff (x² + y² + z²)²dV, where B is the ball with center the origin and radius 5. S the cones. 28. Find the a its center. 29. (a) Find t Ф= 1 (b) Find t 30. Find the v x² + y² + z = √x² 31. (a) Find t stant c (b) Find t 32. Let H be a point is pr (a) Find t (b) Find t (c) Find t 33. (a) Find t radius (b) Find t diame 34. Find the m radius a if distance fr 35-40 Use cy more appropria 35. Find the v cone z = 36. Find the v radius a by angle of T 37. A solid cy height h. (a) Find t (b) Find th of its
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