SalasSV_09_05_ex_ans

# SalasSV_09_05_ex_ans - A-68 9 ANSWERS TO ODD-NUMBERED...

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Unformatted text preview: A-68 9. ANSWERS TO ODD-NUMBERED EXERCISES 11. 1 π 2 1 1 13. 1 15. [2, π] 3 4 π 1 1 [–2,0] 2 [–2, π ] 3 4 17. 19. 2 3 1 1 21. 1 23. θ= π 1 2 θ= π 1 5 25. 3 2 1 2 27. 29. 2 θ= π 3 31. 1 3 1 1 1 1 3 θ= π 4 3 33. yes; [1, π ] = [−1, 0] and the pair r = −1, θ = 0 satisﬁes the equation 35. yes: the pair r = 1 , θ = 1 π satisﬁes equation 2 2 √ 33 ,) 44 π 6 37. [2, π ] = [−2, 0]. The coordinates of [−2, 0] satisfy the equation r 2 = 4 cos θ , and the coordinates of [2, π ] satisfy the equation r = 3 + cos θ . 39. (0, 0), (− 1 , 1 ) 22 41. (−1, 0), (1, 0) √ 43. (0, 0), ( 1 , ± 1 3rt ) 4 4 45. (0, 0), ( ± 47. center: (b, a); radius: 5π 6 √ a2 + b 2 49. (b) The curves intersect at the pole and at [1. 175, 0. 176], [1. 86, 1. 036], [0. 90, 3. 243]. 53. (b) The curves intersect at the pole and at: r = 1 − 3 cos θ [−2, 0] [3. 800, 3. 510] [2. 412, 4. 223] [−1. 267, 0. 713] SECTION 9.5 1. 17. π/6 π /3 1 π a2 4 5π/6 51. θ = , π, 2 55. butterﬂy 57. a petal curve with 2m petals r = 2 − 5 sin θ [2, π ] [3. 800, 3. 510] [−2. 412, 1. 081] [−1. 267, 0. 713] 3. 12 a 2 5. 1 π a2 2 7. 19. 1 4 − 1 π 16 1 ([4]2 2 9. 3 π 16 + 3 8 11. 52 a 2 π /3 13. 1 (3e2π 12 − 3 − 2π 3 ) + π /2 π/3 15. 1 2π (e 4 + 1 − 2eπ ) 1 ([4 sin θ ]2 2 − [2]2 ) d θ π /3 −π/3 π /6 − [2 sec θ ]2 ) d θ + π /2 π/6 1 (1 2 21. 2 0 1 (2 sec θ )2 d θ 2 π /4 0 1 (4)2 d θ 2 √ 3 16 23. 0 1 (2 sin 3θ )2 d θ 2 25. 2 0 1 ( sin θ )2 d θ 2 π /4n 0 − sin θ )2 d θ 27. π − 8 1 ( cos 2θ )2 d θ 2 π /4n 0 29. π 6 − 31. For r = a cos 2nθ , area of one petal is a2 Total area = 35. (5/6, 0) π a2 . 2 37. 9π 2 39. cos2 2nθ d θ = π a2 . For r = a sin 2nθ , area of one petal is a2 8n sin2 2nθ d θ = π a2 . 8n √ 4π +2 3 3 41. (a) Substitute x = r cos θ , y = r sin θ into the equation and solve for r . (c) 8 − 2π SECTION 9.6 1. 4x = ( y − 1)2 3. y = 4x2 + 1, x ≥ 0 5. 9x2 + 4y2 = 36 7. 1 + x2 = y2 9. y = 2 − x2 , −1 ≤ x ≤ 1 11. 2y − 6 = x, −4 ≤ x ≤ 4 ...
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