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SalasSV_08_SkillReview_ans

# SalasSV_08_SkillReview_ans - A-112 21 ANSWERS TO...

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Unformatted text preview: A-112 21. ANSWERS TO ODD-NUMBERED EXERCISES 23. 9 9 2 2 1 1 + g 2 (x ) + C 2 25. 1 8 27. 4 − 64/3 4 29. 19 3 31. 9 2 33. 1 9 3 35. 3 4 37. (a) −1 1 2 + x − x2 dx = 39. (a) 1 4 2 2(x − 1) dx + 2(x − 1) − x + 5 dx (b) −2 2 − y + y dy + 43. 2 2 − y dy 45. (a) −1 2 π r3 3 (b) −2 y + 4 − 1 y2 dy = 18 2 47. 8 + π2 2π y= 64 21 41. 1 1 + x2 2x 1 − 1 + x4 1 + x2 57. (a) (b) f (x) = − sin x √ 59. 3 3 13 2 49. 4 π 15 51. 6 π 7 53. π − 1 π 2 4 65. x = y = 16 ; 35 55. 2π (b) 16 π 35 43 r 3 61. x = 16 , 15 63. x = 0, y = 1 π 8 the two volumes are equal: V = 67. inches 69. 1100 ft-lbs ANSWERS, SKILL MASTERY REVIEW THREE (p. 512) 1. f −1 (x) = (x − 2)3 7. f (x) = 3. f is not one-to-one 1 2 5. f (x) = −ex < 0 on (−∞, ∞); ( f −1 ) (1 + ex )2 11. ex − e3x (1 + e2x )2 13. 1 2 = −4 3x2 + 3x ln 3 x 3 + 3x 3 − 4 ln |x + 1| + C x 23. − 2 cos3 x + C 3 33. π 12 √ 4 + x2 > 0 on (−∞, ∞); ( f −1 ) (0) = x tanh x − ln ( cosh x) x2 17. 2 3 9. 24 [ln x]2 x 15. ( cosh x)1/x 25. 35. 1 2 19. 2[x cosh x − sinh x] + C 1 2 21. 4 ln |x| + − 1 e −2 4 41. 1 2 [x ln |x + 1| − x + ln |x + 1|] + C √ 37. − 27. ln | sec x| − sin2 x + C 39. 1 6 29. 3 4 31. − 1 [ln ( cos x)]2 + C 2 ln 2 + √ 3− 1 4 x 2x 2x − +C ln 2 (ln 2)2 1 2 a2 − x 2 − sin−1 x 45. 1 π 2 1 2 x +C a tan6 x + C 49. x = ln 3 43. sin−1 x − 1 2 √ √ x 1 − x2 − 1 − x2 + C 47. a2 ln 2 √ 6−3 3 3 ln 3 , y= π 2π 51. (b) A = 2 (c) x = 1 π , y = 5 π 2 8 53. [1 − ln 4 + e2 (1 + ln 4)] 55. (a) f increases on (−∞, −1] and [0, 1]; f decreases on [ − 1, 0] and [1, ∞]; (b) absolute max: f (−1) = f (1) = e−1 ; absolute min: f (0) = 0 √ √ √ (c) concave up on −∞, − 1 5 + 17 , − 1 5 − 17, 1 5 − 17 , and 2 2 2 √ √ and 1 5 − 17, 1 5 + 17 2 2 (d) 1 2 5+ √ 17, ∞ ; concave down on − 1 5 + 2 √ 17, − 1 5 − 2 √ 17 0.2 –4 –2 2 4 57. T = − ln 2 ∼ = 3. 1 years ln 0. 8 59. (a) 6.94 grams (b) 18,935 years ago ANSWERS, SKILL MASTERY REVIEW FOUR (p. 704) 1. 2 1 –4 –3 –2 –1 –1 –2 –2 –1 –1 –2 –3 3. 2 1 1 2 6π 9 π 4 ...
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