Mat125-Chapter1 Homework Solution (Loi giai) Odd

Mat125-Chapter1 Homework Solution (Loi giai) Odd - Answers...

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Unformatted text preview: Answers to Odd-Numbered Problems, Chapter Checkup Problems, and Odd—Numbered Chapter Review Problems CHAPTER 1 Section 1 51. in.) = 2 ~xig<u> = <75 +3 1- f(0) = —2;f(-2) = mm = 6 53. a. f(2) = 46 3. g(—1>= —2;g(1>= 212(2):; '0' 7(2) ’1“) = 26 5. 71(2) = 2%; 71(0) = 2; h(—4) = 2V3 ANSWERS 97 55. a. P(9) = -5‘; 19,400 people _ . _ L. _ _1_ _ = L. 7. f(1) — 1,f(5) — 27,f(13) — 125 b. P(9) P(8) 15, 67 people 9, f(1) = 0; f0) = 2; f(3) = 2 . P(t) approaches 20 (20,000 people) 11. f(—6) —_— 3;f(—5) = —4;f(16) = 4 57. . 5(0) = 25.344 cm/sec 13, Yes . S(6 x 10—3) = 19.008 om/sec 15. No,f(t) is not defined fort > 1 - 5(8) 15-8 z 6 596963 . $2 = V151 . Approximately 41,000 square miles 59. 17. All real numbers x except x = —2 19' All real numbers )6 for Wthh x Z — 3 61. . All real numbers x except x = 200 c a b a b c a 21. All real numbers tfor which —3 < t < 3 b. All real numbers x for which 0 s x s 100 23- f(g(x)) = 3x2 + 14x + 10 c. C(50) = $50 million d e a b c a 25. f(g(x)) = x3 + 2x2 + 4x + 2 . C(100) — C(50) = $100 million . C(x) = 37.5 million implies thatx = 40% . C(p(t)) = 4.2 + 0.08;2 . c(p(2)) = 4.52 parts per million . 5 years 1 27. f(g(x)) — (x _1)2 _ 61 29. f(g(x)) = lxl .f(x+h)-f(X)=2x+h 31 h 65. . R(x) = —0.02x2 + 29x; _ _ P(x) = —1.45x2 + 10.7): — 15.6 33_ w: 1 b. P(x)>0if2<x<5.38 h xl" + h) 67 a R(x) = —0 5x2 + 39x' 35. 70:0» = V1 — 33c; g(f(X)) = 1 — 3W; ' ' P(x) = —238 + 29.8.5— 67 f(g(X>) = $000) I” = 0 b. P(x) > 0 if 2.76 < x < 12.14 37- f(g(X)) = x; g(f(X)) = x;f(g(X)) =-g(f(x)) for all 4 374 real numbers exceptx = 1 andx = 2 69. a. Q(P(t)) = (0 0412 +7 0 2t + 12)2 __ —— 2 _. ' I 39- f (x 2) — 2x 11" + 15 b. Q(p(10)) = 13.5 kilograms/week 41. f(x—1)=x5—3x2+6x—3 c, 7:0 43. f(x2 + 3X ’ 1) = W 71. All real numbersxexceptx = l andx = —1.5 45. N + 1) = x 73. f(g(2.3)) = 6.31 x + 1 Note: In answers 47 to 51, answers may vary. 47. h(x)=x—1;g(u)=u2+2u+3 49. h(x) = x2 + 1; g(u) =i 671 s—2 ' 672 Answers U) 75. a. n: I.” Level of 3 Education \ Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 w No high school diploma 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2 High school diploma 1.45 1.41 1.52 1.48 1.53 1.48 1.42 1.47 1.52 1.45 < Some college 1.63 1.63 1.68 1.62 1.70 1.68 1.63 1.72 1.76 1.67 Bachelor’s degree 2.48 2.55 2.74 2.72 2.64 2.54 2.51 2.73 2.83 2.76 Advanced degree 3.65 . 3.80 4._35 __ 4.10 ‘i04 _ ‘ 4.08 __ 3.92- . 3.95 _ 4.20 3.85 b. 1.45, 1.67, 2.76, 3.85 7. f(x)=2x-l CHAPTER 1 Section 2 1. a. Power function h. Polynomial c. Polynomial d. Rational function 3. f(x) = x y (070)\ :(1, 1) 5. f(x) = x3 15. f(x) = { x-l x+1 ifo ifx>0 0 19. y=3x+5andy=—x+3; Answers 17 2’2 21. y = x2 andy = 3x — 2; (2, 4) and (1, 1) y 23. 3y—2x=5andy+3x=9;(2,3) 25. a. b. c. d. 27. a. b. c. d. y (0, —1) (1, 0) f(x) = 3 whenx = f(x) = —3 when x (0, 2) (-1, 0), (3.5, 0) f(x) = 3 when x = f(x) = -3 whenx 4 673 ANSWERS 674 Answers 29. P(p) = (p — 40)(120 — p); optimal price is $80 per 31. 33. recorder (80, 1,600) a. E(p) = —200p2 + 12000;; E 2 X 105 (30, 180000) b. The p intercepts represent prices at which con- sumers spend no money on the commodity. c. $30 per unit a. P(x) = —0.07x2 + 35x — 574.77 P ($100) 4 000 (250, 3800.23) x000) 250 b. 25,000 units; $25.50 35. D(v) = 0.065122 + 0.148v D 700 350 v 0 50 100 37. a. R(p) = —0.05p2 + 210p b. R 250,000 (2,100, 220, 500) 1 25.000 2,000 c. $2,100 per month; $220,500 39. a. N 5 ,000 2,500 t 0 10 20 b. 3,967 thousand tons c. 4.27 years after 1990, or in March 1994. d. No, the formula predicts negative emissions after December 2004. 41. Function 43. 45. Not a function Answers will vary. 676 Answers ANSWERS 13. 15. . M4.- 11. Slope: undefined; intercepts: (3, 0) 19, 21. 23. 25. 27. 29. 31. 33. 35. -45 43 y=§x+§ y=5 y=—2x+9 y=x+2 y = C(x) = 60x + 5,000 37. a. y = f(t) = 35: + 220 b. Y y (0, 5,000) 325 y (0, 220) 39. f(t) = —150t + 1,500 (0, 1,500) S—6 ‘4 -<«- .- '=;,j§ 3;] d-‘rer-[L Answers 679 S-9 2,400 if 1 s x s 40 Optimal price is $25.50. The manufacturer will U) 1 actually make more profit by reducing the price by D: 27. R(x) = x<80 — 5x) if 40 < x < 80 $4.50 per unit. ”g . 5,12 40x lfx 2 80 37. C(x) = 20x + O W x Z R c 4. 4,000 4,000 2,500 i 2.000 3 (16, 640) 333 3‘13 0 . 40 80 100 x 3 3 0 20 40 . .3 . ‘ < 5 .15 29. a. C (x) = 3 50X fo 50 The number of machines is 16 1 f3 3x 1fx 2 50 3 .3 39. R(x) = (3 — 0.02x)(l40 + x), wherex = days from 2 3 C 1 : July 1 . j 300 ‘3 3 R - ‘. 450 (5. 420.5) ‘ 3 20° (49, 171.5) 420 3 .3 ‘50 (50, 150) , 3 X 0 50 100 D. $21.50 x ,3 0 5 150 x‘ 31. V(x) = 4x — -3— Farmer should harvest when x = 5 or July 6 ‘ 100 41. a. x‘. = 25; p3, = 225 33. A(x) = 8x + T + 57 b. p 35. P(p) = (33.000 — 1,000p)(p — 18) 275 P($1.000) 60 (25, 225) 150 30 X 0 20 40 c. 0<x<25;x>25 0 18 25.5 33 p ANSWERS 680 43. a. x, = 9; p, = 25.43 45. 47. 49. 51. 53. 55. Answers D(x) S (x) . O<x<9;x>9 a. xe=10;pc=35 385 D(x) S (x) c. 8(0) = 15; No units will be produced until the price is at least $15. 2 hours, 45 minutes after the second plane leaves If N 5 6,000 or N 2 126,000, choose publisher A, otherwise publisher B. I = k7'1'r2 m =———x+ y Rm Rm 4000 a. x 2,000 C (x) 85,200 96,200 107,200 1 1 8,200 4,000 . x 78,000 1 17,000 156,000 39,000 c. C(x) = 5.5x + 74,200 d. R(x) = 19.5x 6,000 8,000 8,000 ,000 6,000 R(X) y = R(X) CHAPTER 1 Section 5 1. lim f(x) = b .\'—>(l 3. lim f(x) = b .\‘—>u 5. Limit does not exist. 7. 4 9. 7 11. 16 13. i 7 15. Limit does not exist. 17. 2 l9. 7 5 21. 3 23. 5 25. l 4 27. +00; —00 29. —00; —°° 1 1 31. 2; 2 33. 0; 0 35. +00; —00 37. 1; —1 39, x 1.9 1.99 1.999 2.001 V 2.01 f(x) 1.71 1.9701 1.997001 >< 2.003001 2.0301 2.31 .1er1f<x>= 2 f. C(x) = R(x) = $103,350 when x = 5,300 books g. Approximately 4,359 books must be sold for a revenue of $85,000. The “profit” is actually a loss of $13,174. S—1 0 ...
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