Chapter Test AN101 31. Using left endpoints: n 2: 0 0.5 0.5; = + = n 4: 0 0.125 0.25 0.375 0.75; = + + + = ( ) = + + + + + = + = n 10: 0 0.02 0.04 0.06 0.18 10 2 0 0.18 0.9; = + + + + + n 100: 0 0.0002 0.0004 0.0006 0.0198 ( ) = + = 100 2 0 0.0198 0.99 Using right endpoints: n n 2: 0.5 1 1.5; 4: 0.125 0.25 0.375 0.5 1.25; = + = = + + + = ( ) = + + + + = + = n 10: 0.02 0.04 0.06 0.20 10 2 0.02 0.20 1.1; = + + + + n 100: 0.0002 0.0004 0.0006 0.02 ( ) = + = 100 2 0.0002 0.02 1.01 Review Exercises (page 975) 1. 9 2. 25 3. 4 4. 0 5. 64 6. − 1 4 7. 1 3 8. 6 7 9. 0 10. 3 2 11. 28 11 12. Continuous 13. Not continuous 14. Not continuous 15. Continuous 16. { } − ≤ < < < < ≤ x x x x | 6 2 or 2 5 or 5 6 17. All real numbers 18. 1, 6 19. 4 20. ( ) ( ) − = − = f f 6 2; 4 1 21. 4 22. −2 23. −∞ 24. ∞ 25. Does not exist 26. No 27. Yes 28. R is discontinuous at = − x 4 and = x 4. R x lim 1 8 : x 4 ( ) = − →− hole at 4, 1 8 ( ) − − R x R x lim ; lim : x x 4 4 ( ) ( ) = −∞ =∞ → → − + The graph of R has a vertical asymptote at = x 4. 29. Undefined at = x 2 and = x 9; R has a hole at = x 2 and a vertical asymptote at = x 9. 33. −24 34. −3 35. 7 36. −158 37. 0.66625 38. (a) 7 sec (b) 6 sec (c) 64 ft/sec (d) t 32 96 ft/sec ( ) − + (e) 32 ft/sec (f) At = t 3 sec (g) 96 ft/sec − (h) 128 ft/sec − 39. (a) $61.29/watch (b) $71.31/watch (c) $81.40/watch (d) ( ) = − + − R x x x 0.25 100.01 1.24 2 (e) Approximately $87.51/watch 30. = m 12 tan y x 10 21 (1, 10) y 5 12x 2 2 f(x) 5 2x2 1 8x 31. = m 0 tan y x 5 5 (21, 24) y 5 24 f(x) 5 x2 1 2x 2 3 32. = m 16 tan y x 5 21 f(x) 5 x3 1 x2 y 5 16x 2 20 (2, 12) 33. y x 8 22 4 24 f(x) 5 log 2 x 34. ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 19 22 2 43 50 4 35. + + x h 4 2 3 36. ( ) − − + − + x x x 1 2 1 2 4 2 2 y x 5 5 x 5 4 y 5 0 44. (a) Area under the graph of ( ) = f x ex from −1 to 1 (b) y x 2.5 4 (c) 2.35 Chapter Test (page 977 ) 1. −5 2. 1 3 3. 5 4. −2 5. 135 6. 2 3 7. −1 8. −3 9. 5 10. 2 11. Limit exists; 2 12. (a) Yes (b) No; ( ) ( ) ≠ → f x f lim 1 x 1 (c) No; ( ) → f x lim x 3 does not exist. (d) Yes 13. x 7: = − asymptote; x 2: = hole 14. (a) 5 (b) = − y x5 19 (c) y x 5 30 (2, 29) y 5 5x 2 19 f(x) 5 4x2 2 11x 2 3 15. (a) y x 5 5 (b) 13.359 (c) π ≈ 4 12.566 16. ∫ ( ) − + + x x dx 5 3 1 4 2 17. 106 3 ft/sec 40. (a) y x 5 14 (b) 24 (c) 32 (d) 26 (e) 30 (f) 28 41. (a) y x 3 5 (b) 10 (c) 77 8 (d) ∫ ( ) − − x dx 4 1 2 2 (e) 9 42. (a) y x 4 2 (b) ≈ 49 36 1.36 (c) 1.02 (d) ∫ x dx 1 1 4 2 (e) 0.75 43. (a) Area under the graph of ( ) = − f x x 9 2 from −1 to 3 (b) y x 4 10 (c) 80 3
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