AN100 Answers: Chapter 14 17. (a) y x 5 1.5 (b) 25 12 (c) 4609 2520 (d) ∫ x dx 1 1 5 (e) 1.609 19. (a) y x 4 20 (b) 11.475 (c) 15.197 (d) ∫ − e dx x 1 3 (e) 19.718 21. (a) y 1.2 x P (b) 1.896 (c) 1.974 (d) ∫ π xdx sin 0 (e) 2 23. (a) Area under the graph of ( ) = + f x x3 1 from 0 to 4 (b) y x 5 16 (c) 28 25. (a) Area under the graph of ( ) = − f x x 1 2 from 2 to 5 (b) y x 5 30 (c) 36 27. (a) Area under the graph of ( ) = f x x sin from 0 to π 2 (b) y 1.5 x P (c) 1 29. (a) Area under the graph of ( ) = f x ex from 0 to 2 (b) y x 4 8 (c) 6.389 9. = m 3 tan y x 5 10 f(x) 5 3x 1 5 (1, 8) 11. = − m 2 tan y x 5 10 y 5 22x 1 1 f(x) 5 x2 1 2 (21, 3) 13. = m 12 tan y x 5 15 (2, 12) f(x) 5 3x2 y 5 12x 2 12 15. = m 5 tan y x 5 8 (1, 3) y 5 5x 2 2 f(x) 5 2x2 1 x 17. = − m 4 tan y x 5 10 y 5 24x 1 2 (21, 6) f(x) 5 x2 2 2x 1 3 19. = m 13 tan y x 5 18 f(x) 5 x3 1 x y 5 13x 2 16 (2, 10) 21. −4 23. 0 25. 7 27. 7 29. 3 31. 1 33. 60 35. −0.8587777 37. 1.389623659 39. 2.362110222 41. 3.643914112 43. 18 ft/ft 3 π 45. 16 ft/ft 3 π 47. (a) 6 sec (b) 64 ft/sec (c) t 32 96 ft/sec ( ) − + (d) 32 ft/sec (e) 3 sec (f) 144 ft (g) 96 ft/sec − 49. (a) 70 3 ft/sec − (b) 21 ft/sec − (c) 18 ft/sec − (d) ( ) = − − + s t t t 2.631 10.269 999.933 2 (e) Approximately 15.531 ft/ sec − 14.5 Assess Your Understanding (page 973) 3. ∫ ( ) f x dx a b 4. b 5. 3 7. 56 9. (a) y x 8 24 (b) 36 (c) 72 (d) 45 (e) 63 (f) 54 11. (a) y x 4 10 (b) 18 (c) 9 (d) 63 4 (e) 45 4 (f) 27 2 13. (a) y x 5 20 (b) 22 (c) 51 2 (d) ∫ ( ) + x dx 2 0 4 2 (e) 88 3 15. (a) y x 5 90 (b) 36 (c) 49 (d) ∫ x dx 0 4 3 (e) 64 51. Vertex: 1, 3 ; ( ) focus: 1, 7 2 ( ) 52. ( ) ( ) − 2, 6 , 1, 3 53. 10 54. 23.66 sq. units 14.4 Assess Your Understanding (page 966) 3. tangent line 4. derivative 5. c 6. T 7. T 8. T 77. = − x 2: 3 asymptote; x 1: = hole 79. x 3: = − asymptote; x 2: = hole 81. = − x 2: 3 asymptote; x 1: = − hole 91. Vertical: = x 4; horizontal: = y 3 92. 60 93. ( ) x y z ln 5 2 4 94. − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 3 1 2 1 0 2 0 1 3 4 5 2 83. 3 23 23 5 85. 20 220 220 20 87. 3 23 22 1
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