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Spring_calculus_12_Selected_Answers_2up

Spring_calculus_12_Selected_Answers_2up - 296 Appendix A...

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A Selected Answers 1.1.1. (2 / 3) x + (1 / 3) 1.1.2. y = 2 x 1.1.3. ( 2 / 3) x + (1 / 3) 1.1.4. y = 2 x + 2, 2, 1 1.1.5. y = x + 6, 6, 6 1.1.6. y = x/ 2 + 1 / 2, 1 / 2, 1 1.1.7. y = 3 / 2, y -intercept: 3 / 2, no x -intercept 1.1.8. y = ( 2 / 3) x 2, 2, 3 1.1.9. yes 1.1.10. y = 0, y = 2 x + 2, y = 2 x + 2 1.1.11. y = 75 t , 164 minutes 1.1.12. y = (9 / 5) x + 32, ( 40 , 40) 1.1.13. y = 0 . 15 x + 10 1.1.14. 0 . 03 x + 1 . 2 1.1.15. (a) y = braceleftBigg 0 0 x < 100 ( x/ 10) 10 100 x 1000 x 910 1000 < x 1.1.16. y = braceleftBigg 0 . 15 x 0 x 19450 0 . 28 x 2528 . 50 19450 < x 47050 0 . 33 x 4881 47050 < x 97620 1.1.17. (a) P = 0 . 0001 x + 2 (b) x = 10000 P + 20000 1.1.18. (2 / 25) x (16 / 5) 1.2.1. (a) x 2 + y 2 = 9 (b) ( x 5) 2 + ( y 6) 2 = 9 (c) ( x + 5) 2 + ( y + 6) 2 = 9 1.2.2. (a) Δ x = 2, Δ y = 3, m = 3 / 2, y = (3 / 2) x 3, 13 (b) Δ x = 1, Δ y = 3, m = 3, y = 3 x + 2, 10 (c) Δ x = 2, Δ y = 2, m = 1, y = x , 8 1.2.6. ( x + 2 / 7) 2 + ( y 41 / 7) 2 = 1300 / 49 1.3.1. { x | x 3 / 2 } 295 296 Appendix A Selected Answers 1.3.2. { x | x negationslash = 1 } 1.3.3. { x | x negationslash = 1 and x negationslash = 1 } 1.3.4. { x | x < 0 } 1.3.5. { x | x R } , i.e., all x 1.3.6. { x | x 0 } 1.3.7. { x | h r x h + r } 1.3.8. { x | x 1 } 1.3.9. { x | − 1 / 3 < x < 1 / 3 } 1.3.10. { x | x 0 and x negationslash = 1 } 1.3.11. { x | x 0 and x negationslash = 1 } 1.3.12. R 1.3.13. { x | x 3 } , { x | x 0 } 1.3.14. A = x (500 2 x ), { x | 0 x 250 } 1.3.15. V = r (50 πr 2 ), { r | 0 < r radicalbig 50 } 1.3.16. A = 2 πr 2 +2000 /r , { r | 0 < r < ∞} 2.1.1. 5, 2 . 47106145, 2 . 4067927, 2 . 400676, 2 . 4 2.1.2. 4 / 3, 24 / 7, 7 / 24, 3 / 4 2.1.3. 0 . 107526881, 0 . 11074197, 0 . 1110741, 1 3(3 + Δ x ) 1 9 2.1.4. 3 + 3Δ x + Δ x 2 1 + Δ x 3 2.1.5. 3 . 31, 3 . 003001, 3 . 0000, 3 + 3Δ x + Δ x 2 3 2.1.6. m 2.2.1. 10, 25 / 2, 20, 15, 25, 35. 2.2.2. 5, 4 . 1, 4 . 01, 4 . 001, 4 + Δ t 4 2.2.3. 10 . 29, 9 . 849, 9 . 8049, 9 . 8 4 . t → − 9 . 8 2.3.1. 7 2.3.2. 5 2.3.3. 0 2.3.4. undefined 2.3.5. 1 / 6 2.3.6. 0 2.3.7. 3 2.3.8. 172 2.3.9. 0 2.3.10. 2 2.3.11. does not exist 2.3.12. 2 2.3.13. 3 a 2 2.3.14. 512 2.3.15. 4 2.3.16. 0 2.3.18. (a) 8, (b) 6, (c) dne, (d) 2, (e) 1, (f) 8, (g) 7, (h) 6, (i) 3, (j) 3 / 2, (k) 6, (l) 2 2.4.1. x/ 169 x 2 2.4.2. 9 . 8 t 2.4.3. 2 x + 1 /x 2 2.4.4. 2 ax + b 2.4.5. 3 x 2 3.1.1. 100 x 99 3.1.2. 100 x 101 3.1.3. 5 x 6 3.1.4. πx π 1 3.1.5. (3 / 4) x 1 / 4 3.1.6. (9 / 7) x 16 / 7 3.2.1. 15 x 2 + 24 x 3.2.2. 20 x 4 + 6 x + 10 /x 3 3.2.3. 30 x + 25
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Appendix A Selected Answers 297 3.2.4. 6 x 2 + 2 x 8 3.2.5. 3 x 2 + 6 x 1 3.2.6. 9 x 2 x/ 625 x 2 3.2.7. y = 13 x/ 4 + 5 3.2.8. y = 24 x 48 π 3 3.2.9. 49 t/ 5 + 5, 49 / 5 3.2.11. n summationdisplay k =1 ka k x k 1 3.2.12. x 3 / 16 3 x/ 4 + 4 3.3.1. 3 x 2 ( x 3 5 x + 10) + x 3 (3 x 2 5) 3.3.2. ( x 2 +5 x 3)(5 x 4 18 x 2 +6 x 7) + (2 x + 5)( x 5 6 x 3 + 3 x 2 7 x + 1) 3.3.3. 625 x 2 2 x x x 625 x 2 3.3.4. 1 x 19 625 x 2 20 625 x 2 x 21 3.3.5. f = 4(2 x 3), y = 4 x 7 3.4.1. 3 x 2 x 3 5 x + 10 x 3 (3 x 2 5) ( x 3 5 x + 10) 2 3.4.2. 2 x + 5 x 5 6 x 3 + 3 x 2 7 x + 1 ( x 2 + 5 x 3)(5 x 4 18 x 2 + 6 x 7) ( x 5 6 x 3 + 3 x 2 7 x + 1) 2 3.4.3. 1 2 x 625 x 2 + x 3 / 2 (625 x 2 ) 3 / 2 3.4.4. 1 x 19 625 x 2 20 625 x 2 x 21 3.4.5. y = 17 x/ 4 41 / 4 3.4.6. y = 11 x/ 16 15 / 16 3.4.8. y = 19 / 169 5 x/ 338 3.4.9. 13 / 18 3.5.1. 4 x 3 9 x 2 + x + 7 3.5.2. 3 x 2 4 x + 2 / x 3.5.3. 6( x 2 + 1) 2 x 3.5.4.
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