Calculus 10th Edition Larson Solutions Manual by jacquelineag89

© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. CHAPTER P PreparationforCalculus Section P.1 Graphs and Models................................. 2 Section P.2 Linear Models and Rates of Change....................................................11 Section P.3 Functions and Their Graphs........................ 22 Section P.4 Fitting Models to Data............................ 34 Review Exercises ..........................................................................................................37 Problem Solving ...........................................................................................................43 NOT FOR SALE INSTRUCTORUSE ONLY © Cengage Learning. All Rights Reserved. Calculus 10th Edition Larson Solutions Manual Full Download: http://testbanktip.com/download/calculus-10th-edition-larson-solutions-manual/ Download all pages and all chapters at: TestBankTip.com

NOT FOR SALE

CHAPTER P PreparationforCalculus

Section P.1 Graphs and Models

1. 3 2 3 yx

x-intercept:(2,0)

y-intercept:(0,3) Matchesgraph(b).

2. 2 9 yx

x-intercepts: 3,0,3,0

y-intercept:(0,3) Matchesgraph(d).

3. 2 3 yx

x-intercepts: 3,0,3,0

y-intercept:(0,3) Matchesgraph(a).

4. 3 yxx

x-intercepts: 0,0,1,0,1,0

y-intercept:(0,0) Matchesgraph(c).

1 2 2

6. 52 yx 7. 2 4 yx 8. 2 3 yx 9. 2 yx x 4 2 0 2 4 y 0 1 2 3 4 x 1 0 1 2 5 2 3 4 y 7 5 3 1 0 1 3 x 3 2 0 2 3 y 5 0 4 0 5 x 0 1 2 3 4 5 6 y 9 4 1 0 1 4 9 x 5 4 3 2 1 0 1 y 3 2 1 0 1 2 3 2 424 2 4 6 y x ( 2, 1) ( 4, 0) (0, 2) (2, 3) (4, 4) 2 4 6 2 4 2 4 8 y x ( 1, 7) (0, 5) (1, 3) (2, 1) (3, 1) (4, 3) , 0 5 2( ( x 2 4 2 6 6 4 646 ( 3, 5)(3, 5) ( 2, 0) (0, 4) (2, 0) y 6 4 2 2 2 2 4 4 6 6 8 10 y x (1, 4) (2, 1) (3, 0) (4, 1) (5, 4) (6, 9) (0, 9) x 2 2 4 6 4 62 ( 3, 1) ( 1, 1) ( 4, 2) ( 2, 0) (0, 2) (1, 3) ( 5, 3) y

INSTRUCTOR

USE ONLY ST

3 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 10. 1 yx 11. 6 yx 12. 2 yx 13. 3 y x 14. 1 2 y x 15. 5 yx (a) 2,2,1.735231.73 yy (b) ,34,3354x 16. 5 5 yxx (a) 0.5,0.5,2.47 y (b) ,41.65,4x and,41,4 x 17. 25yx y-intercept: 2055;0,5 y x-intercept: 55 22 025 52 ;,0 x x x 18. 2 43yx y-intercept: 2 4033;0,3 y x-intercept: 2 2 043 34 x x None. y cannotequal0. x 3 2 1 0 1 2 3 y 2 1 0 1 0 1 2 x 0 1 4 9 16 y 6 5 4 3 2 x 2 1 0 2 7 14 y 0 1 2 2 3 4 x 3 2 1 0 1 2 3 y 1 3 2 3 Undef. 3 3 2 1 x 6 4 3 2 1 0 2 y 1 4 1 2 1 Undef. 1 1 2 1 4 3 23 3 4 2 2 2 1 1 y x ( 3, 2) ( 2, 1) ( 1, 0) (0, 1) (1, 0) (2, 1) (3, 2) y x (0, 6) (1, 5) (4, 4) (9, 3) (16, 2) 4481216 2 4 6 8 2 5101520 2 3 4 5 y x ( 2, 0) ( 1, 1) (0, 2) (2, 2) (7, 3) (14, 4) y x (3, 1) (1, 3) ( 3, 1) ( 1, 3) 1 2 3123 1 2 1 2 3 2, 3 2 ( ( 2, 3 2 ( ( 1123 2 3 4 5 2 3 4 5 1 4 6, () 1 2 4, () 1 2 0, () 1 4 2, () ( 3, 1) ( 1, 1) y x 9 6 9 6 ( 0.5, 2.47) (1, 4) 66 3 5 ( 4.00, 3) (2, 1.73)

Section P.1 Graphs and Models

)

NOT FOR SALE Graph INSTRUCTOR USE ONLY S

NOT FOR SALE paration parationCalculus Calc

19. 2 2 yxx

y-intercept: 2 002

20. 23 4 yxx

25. 22 40xyxy y

22 0040

21. 2 16 yxx

y-intercept: 2 01600;0,0 y

x-intercepts: 2 016 044

26. 2 21yxx

Note: 33 x is an extraneous solution.

27. Symmetric with respect to the y-axis because

28. 2 yxx No symmetry with respect to either axis or the origin.

4 Chapter PPreparation for Calculus

be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2;0,2 y y

2,1;2,0,1,0 xx xx x

x-intercepts: 2 02 021

0;0,0

y-intercept: 23040

0,2;0,0,2,0 xx xxx x

x-intercepts: 3 04 022

0,4,4;0,0,4,0,4,0 xx xxx x

-intercept:

1;0,1

-intercept: 2 011 1;1,0 xx x 23. 2 51 x y x 20 -intercept:2;0,2 501 2 -intercept:0 51 02 4;4,0 yy x x x x x 24. 2 2 3 31 xx y x y-intercept: 2 2 030 301 0;0,0 y y x-intercepts: 2 2 2 3 0 31 3 0 31 0,3;0,0,3,0 xx x xx x x

22. 2 11yxx y

2 0101

-intercept:

0;0,0 yy y

-intercept:

0;0,0 xx x

220400

-intercept: 2

1;0,1 y y x-intercept: 2 2 22 2 2 021 21 41 31 1 3 3 3 33 ;,0 33 xx xx xx x x x x

2001

2 2 66.yxx

29. Symmetric with respect to the x-axis because 2 23 8.yyxx

INSTRUCTORUSE

NOT FOR SALE P.1Graph Sections

30. Symmetric with respect to the origin because

3 3 3

yxx yxx yxx

31. Symmetric with respect to the origin because

4. xyxy

32. Symmetric with respect to the x-axis because

2 2 10. xyxy

33. 43yx

No symmetry with respect to either axis or the origin.

34. Symmetric with respect to the origin because

xyx xyx

40. 2 3 1 yx

2 3

011, -intercept 011, -intercept yy xxxx

3 22 332

Intercepts: 3 2 0,1,,0

Symmetry:none

41. 2 9 yx

40 40.

2 2

35. Symmetric with respect to the origin because

36.

2 1 x y x is symmetric with respect to the y-axis because

1 xx y xx

37. 3 yxx is symmetric with respect to the y-axis because 3 33 yxxxxxx

38. 3 yx is symmetric with respect to the x-axis because 3 3. yx yx

39. 23 yx 2 3

2302,-intercept 02332,-intercept yy xxxx

Intercepts: 2 3 0,2,,0

Symmetry:none

2 22

909,-intercept 0993,-intercepts yy xxxx

Intercepts:0,9,3,0,3,0 2 2 99 yxx

Symmetry: y-axis

42. 2 221yxxxx 1 2

02010,-intercept 0210,,-intercepts yy xxxx

Intercepts: 1 2 0,0,,0

Symmetry:none

43. 3 2 yx 3

33 022,-intercept 0222,-intercept yy xxxx

Intercepts: 3 2,0,0,2

Symmetry:none

Section P.1Graphs and Models 5

2 2 1 1

x x y x

x y

2 2 2 2

(0, 2) 2 1 x 3 2 1 1 , 0 2 3 y ( ( 1 1 12 2 2 y x 3 2 , 0 () (0, 1) y x (3, 0) (0, 9) ( 3, 0) 2 4 6246 2 2 4 6 10 1 2 3 1 2 3 1 3 5 2 4 (0, 0) 1 2 , 0 () y x y x (0, 2) 2 3123 1 1 3 4 5 3 ( 2, 0)

INSTRUCTORUSE

ONLY ©

44. 3 4 yxx

3 0400,-interceptyy

47. 3 x y

xx xx xxx xx

40 40 220 0,2,-intercepts

3 2

Intercepts:0,0,2,0,2,0

3 33 444 yxxxxxx

Symmetry:origin

45. 5 yxx 0050,-intercept 500,5,-intercepts yy xxxx

Intercepts:0,0,5,0

Symmetry:none

46. 2 25 yx

2 250255,-interceptyy

3 00,-intercept 0,-intercept yyy xx Intercept:(0,0)

Symmetry:origin

40 220 2,-intercepts 044,-intercept

2 2

x x xx xx

250 250 550 5,-intercept

Intercepts:0,5,5,0,5,0

2 2 2525 yxx

Symmetry: y-axis

6 Chapter PPreparation

for Calculus

3 3 x yxy

48. 2 4

2 2

x-axis 49. 8 y x 8

0 8 0Nosolutionno-intercept yy x x Intercepts:none

yy xx Symmetry:origin y x 1 2 3 412 3 4 2 3 ( 5, 0)(0, 0) 1 2 3 412345 2 3 1 2 3 4 6 7 y x (0, 5) (5, 0) ( 5, 0) x 1 2 3 4 2 3 4 2 1 3 4234 (0, 0) y 1 3 3 1 2 5 ( 4, 0) (0, 2) y x (0, 2) y x 22468 2 4 6 8 3 3 1 1 2 1 3 3 ( 2, 0)(2, 0) (0, 0) y x

INSTRUCTOR USE ONLY NSTR 4 1234 5 2345 TNS R S © Cengage

Rights Reserved.

yy yy xx Intercepts:0,2,0,2,4,0

44xyy Symmetry:

Undefinedno-intercept

NOT FOR SALE paration parationCalculus Calc

Learning. All

NOT FOR SALE P.1Graphs

Section P.1Graphs and Models 7 ©

Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 50. 2 10 1 y x 2 10 10,-intercept 01 yy 2 10 0Nosolutionno-intercepts 1 x x Intercept:(0,10) 2 2 1010 1 1 y x x Symmetry: y-axis 51. 6 yx 606,-interceptyy 60 6 6,-intercepts x x xx Intercepts: 0,6,6,0,6,0 66 yxx Symmetry: y-axis 52. 6 yx 6066,-interceptyy 60 60 6,-intercept x x xx Intercepts:(0,6),(6,0) Symmetry:none 53. 2 2 9 9 9 yx yx yx 0993,-intercepts 90 90 9,-intercept yy x x xx Intercepts: 0,3,0,3,9,0 2 2 99yxyx Symmetry: x-axis 54. 2 22 4 44 2 x xyy 2 2 2 2 404 1,-intercepts 22 404 4 2,-intercepts yy x x xx Intercepts: 2,0,2,0,0,1,0,1 22 22 4444xyxy Symmetry:originandbothaxes 6 4 2 2 2 12 10 46 (0, 10) y x x 2 2 4 2 6 8 4 6 8 4 2 8468 ( 6, 0) (0, 6) (6, 0) y 2 2 4 4 68 8 y x (0, 6) (6, 0) y x ( 9, 0) (0, 3) (0, 3) 2 4 6 102 2 4 6 2 4 6 y x (0, 1) (2, 0) (0, 1) ( 2, 0) 1 313 2 3 2 3

2014 Cengage Learning. All

INSTRUCTORUSE

ONLY

NOT FOR SALE

57. 88 4747 x yyx xyyx 847 155 3

58.

xx x

Thecorresponding y-valueis 5. y Pointofintersection:(3,5)

324

Pointofintersection: 2,1

59. 22

Thecorrespondingy-valuesare

Pointsofintersection: 2,2,1,5

Thecorresponding

Pointsofintersection: 1,2,2,1

8 Chapter PPreparation for Calculus

be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2 2 36 36 6 3 xy yx x y 2 60 2,-intercepts 3 306 6,-intercept yy x xx Intercepts: 6,0,0,2,0,2 2 2 3636xyxy Symmetry: x-axis 56. 2 2 3 4 348 438 2 xy yx yx 2 3 022 4 nosolutionno-intercepts 3408 38 8 3,-intercept y y x x xx Intercept: 8 3,0 2 2 348348 xyxy

x-axis

55.

Symmetry:

2 410

2 x

x x

4210

xyy

xyy 34410 22 34410 714 2 xx xx

Thecorresponding y-valueis 1. y

2,1

xyyx xx xx xx x

66 44 64 02 021

xyyx

2for2yx and 5for1.yx

2 2 2

1 31 321

1or2 xyyx yx xx xxx xxxx xx

60. 22

0212

y-valuesare 2for1yx and 1for2.yx

y x (6, 0) ( ) 0, 2 ( ) 0, 2 112367 2 3 4 1 2 3 4 y x 226810 2 4 6 2 4 6 ( , 0) 8 3

NOT FOR SALE P.1Graphs

Thecorresponding y-valuesare 2 y for1 x and 1 y for2. x

Pointsofintersection: 1,2,2,1 62. 2222

Section P.1Graphs and Models 9

website,

in whole or in part.

xxx xxxx xx

61. 2222 2 2 22 2 55 11 51 521 0224212 1or2 xyyx xyyx xx

054

yyx xyyx xx xxx xx xx xx xx

2 22 2 2 2525 315315 25315 25990225 01090200 0920

4or5 x

32 2131 20 210 1,0,2. xxxxx xxx xxx x 64.

Analytically, 242 42 2 121 0 011 1,0,1. xxx xx xxx x 65. 2 6 4 yx yxx

Analytically, 2 2 2 64 64 560 320 3,2. xxx xxx xx xx x 66. 236 6 yx yx

Analytically, 2366 23 x x xx 23or23 3or1. xxxx xx 4 6 8 4 (2, 1) y = x2 + 3x − 1 y = x3 2x2 + x 1 (0, 1) ( 1, 5) 33 2 2 (1, 0) ( 1, 0) (0, 1) y = 1 x 2 y = x 4 2x 2 + 1 7 2 4 2 x + 6 y = x 2 4x ( 2, 2) y = (3, )3 4 8 7 1 y = 6 x y = 2x 3+ 6 (1, 5) (3, 3)

Thecorresponding y-valuesare 3 y for4 x and 0 y for5. x Pointsofintersection: 4,3, 5,0 63. 32 2 21 31 yxxx yxx Pointsofintersection: 1,5,0,1,2,1 Analytically, 322

21 1 yxx

Pointsofintersection: 1,0,0,1,1,0

Pointsofintersection: 2,2,3,33,1.732

Pointsofintersection:(3,3),(1,5)

INSTRUCTORUSE ONLY

67. (a) Usingagraphingutility,youobtain 2 0.0050.272.7.ytt

(b)

71. 3ykx

(a) 3 1,4:414 kk

(b) 3 1 8 2,1:128kkk

(d) 3 1,1:111 kkk

t y

TheGDPin2020willbe$21.5trillion.

68. (a) Usingagraphingutility,youobtain 2 0.2412.640.ytt

(b)

72. 2 4 ykx

(a) 2 1 4

1,1:141 14 k k k

69.

Themodelisagoodfitforthedata.

t y

Thenumberofcellularphonesubscribersin2020 willbe554million.

2.0456003.29 56003.292.04

56001.25 5600 4480 1.25

CR xx xx x x Tobreakeven,4480unitsmustbesold.

70. 2 10,770 0.37 y x

Ifthediameterisdoubled,theresistanceischangedby approximatelyafactorof 1 4 Forinstance, 2026.555 y and 406.36125. y

(b) 2 2,4:442 168 2

k k k

3,3:343 912 k k k

(d) 2 93 124

73. Answers may vary. Sample answer: 438yxxx has intercepts at 4,3,and8.xxx

74. Answers may vary. Sample answer: 35 22 4 yxxx has intercepts at 35 22 ,4,and.xxx

75. (a) If (x, y) is on the graph, then so is ,x y by y-axis symmetry. Because ,x y is on the graph, then so is ,x y by x-axis symmetry. So, the graph is symmetric with respect to the origin. The converse is not true. For example, 3yx has origin symmetry but is not symmetric with respect to either the x-axis or the y-axis.

(b) Assume that the graph has x-axis and origin symmetry. If (x, y) is on the graph, so is ,x y by x-axis symmetry. Because ,x y is on the graph, then so is ,,x yxy by origin symmetry. Therefore, the graph is symmetric with respect to the y-axis. The argument is similar for y-axis and origin symmetry.

10 Chapter PPreparation

Calculus

duplicated, or posted to a publicly accessible website, in

or in part.

for

whole

0 0 16 30 5 20 330 30 0 0 400 100

NOT FOR SALE

76. (a) 3

Interceptsfor:

3 32

-intercept:000;0,0

-intercepts:0111; 0,0,1,01,0

Interceptsfor2:

-intercept:022;0,2

2 2

xx y

-intercepts:02

None.cannotequal0.

(b) Symmetry with respect to the origin for 3 yxx because 3 3 yxxxx

Symmetry with respect to the y-axis for 2 2 yx because 2 2 22.yxx

xxx xxx xxx xy

2 20 210 26

Point of intersection : (2, 6)

Note: The polynomial 2 1 xx has no real roots.

77. False. x-axis symmetry means that if 4,5 is on the graph, then 4,5 is also on the graph. For example, 4,5 is not on the graph of 2 29, xy whereas 4,5 is on the graph.

True. 44.ff

Section P.2 Linear Models and Rates of Change

yxx yy xxxxxxxx

78.

79. True. The x-intercepts are 2 4 ,0. 2 bbac a 80. True. The x-intercept is ,0. 2 b a

1. 2 m 2. 0 m 3. 1 m 4. 12 m 5. 24 6 3 532 m 6. 716 2 213 m x 123567 1 (3, 4) (5, 2) 2 3 4 5 1 2 3 y 1 2 3 4134 1 2 3 5 6 7 y x ( 2, 7) (1, 1) NOT FOR SALE Section P.2Linear Models and Rate INSTRUCTORUSE ONLY © Cengage Learning. All Rights Reserved.

7. 165 , 440 m undefined. Thelineisvertical.

11.

12.

8. 55 0 0 532 m

13. Becausetheslopeis0,thelineishorizontalandits equationis 2. y Therefore,threeadditionalpointsare 0,2,1,2,5,2.

14. Becausetheslopeisundefined,thelineisverticalandits equationis 4. x Therefore,threeadditionalpoints are 4,0, 4,1, 4,2.

15. Theequationofthislineis 731 310. yx yx Therefore,threeadditionalpointsare(0,10),(2,4),and (3,1).

16. Theequationofthislineis 222 22. yx yx

Therefore,threeadditionalpointsare 3,4, 1,0, and(0,2). 17.

12 Chapter P Preparation for Calculus

Cengage

Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Learning. All

21 1 36 2 2 1 13 4 24 m

31 18 44 3 75 3 8 84 m

Thelineishorizontal. 9.

10.

yx yx xy y x (4, 6) (4, 1) 1 212356 1 2 3 4 5 6 7 1123456 1 2 3 4 6 1 (3, 5)(5, 5) y x x 1 2 3 2 3 2 3213 y ( ) 3 4 1 6 , ( ) 1 2 2 3 , 1 1 2 1 2 3 1 5 4 1 4 () , 7 8 3 4 () , y x y x m = 2 (3, 4) m = 1 3 2 m = m is undefined. 4 624810 2 2 4 6 8 2 624 2 4 6 ( 2, 5) m = 3 m = 3 m = 0 m = 1 3 y x x 1 1 2 3 4 1 2 4 5 (0, 3) y

4 3 4312 03412

INSTRUCTORUSE

NOT FOR SALE paration Calculus Calc

Section P.2 Linear Models and Rates of Change 13 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 18. Theslopeisundefinedsothelineisvertical. 5 50 x x 19. 2 3 32 023 yx yx x y 20. 4 40 y y 21. 233 239 311 0311 yx yx yx xy 22. 3 5 42 52036 35140 yx yx xy 23. (a) 1 Slope 3 y x (b) BythePythagoreanTheorem, 22230101000 101031.623feet. x x 24. (a) (b) Theslopesare:295.8293.0 2.8 54 298.6295.8 2.8 65 301.6298.6 3.0 76 304.4301.6 2.8 87 307.0304.4 2.6 98

(c) Average rate of change from 2004 to 2009: 307.0293.014 945 2.8millionperyr (d) For2020,20and162.8293.0337.8million. Equivalently,112.8307.0337.8. ty y 1 2 3 41 1 2 3 4 5 1 (−5, −2) y x x 1234 1 2 3 4 (0, 0) y 12 1 2 3 1 2 3 5 (0, 4) y x y x (3, 2) 1 1 2123456 2 3 4 5 1 2 3 12 1 2 3 1 2 4 5 ( 2, 4) y x 10 ft 30 ft x y t 456789 290 295 300 305 310 Year (4 ↔ 2004) Population (in millions) (4, 293) (5, 295.8) (6, 298.6) (7, 301.6) (8, 304.4) (9, 307)

Thepopulationincreasedleastrapidlyfrom2008to2009.

P.2 Linear Models and Rate INSTRUCTORUSE

NOT FOR SALE Section

ONLY

25. 43yx

Theslopeis 4 m andthe y-interceptis 0,3.

26. 1 1 xy yx

Theslopeis 1 m andthe y-interceptis(0,1).

27. 1 5

520 4 xy yx

Therefore,theslopeis 1 5 m andthe y-interceptis (0,4).

28. 6 5

6515 3 xy yx

Therefore,theslopeis 6 5 m andthe y-interceptis 0,3.

29. 4 x

Thelineisvertical.Therefore,theslopeisundefinedand thereisno y-intercept.

30. 1 y

Thelineishorizontal.Therefore,theslopeis 0 m and the y-interceptis 0,1. 31.

14 Chapter

PPreparation for Calculus

32. 4 x 33. 21yx 34. 1 3 1 yx 35. 3 2 3 1 22 21yx yx 36. 134 313 yx yx 37. 230 23 xy yx x 1 2 312345 2 4 5 6 1 2 y 1235 1 2 1 2 3 y x x 2 112 1 3 1 y 3 3 4 3 2 2 2 1 1 y x (0, 1) x 1 2 1 3 4 2 2 3 4 3 4234 y 48 8 12 16 4 8 12 16 y x 1 x 32 1 2 3 1 2 y

INSTRUCTORUSE

NOT FOR SALE paration parationCalculus Calc

ONLY

Section P.2Linear Models and

of Change 15 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 38. 1 2 260 3 xy yx 39. 80 2 40 020 2 02 m yx yx xy 40. 72 9 3 123 m 232 232 34 034 yx yx yx xy 41. 808 253 m 8 05 3 840 33 83400 yx yx xy 42. 624 1 314 m 211 21 30 yx yx xy 43. 835 660, m undefined Thelineishorizontal. 6 60 x x 44. 22 0 0 312 m 2 20 y y 45. 7311 11 244 11 2 0 22 m 311 0 42 113 24 02243 yx yx xy 46. 31 18 44 3 75 3 8 84 m 185 434 1233240 3212370 yx yx xy 10 8 6 2 4 6 2 4 y x y x 2 4246 2 4 6 8 (4, 8) (0, 0) 4 6246 4 4 6 8 y x ( 2, 2) (1, 7) 1 2 3 4 5 2 6 7 8 9 x 146789 123 (5, 0) (2, 8) y 12 3 1 3 2 4 1 3 2 5 7 6 (1, 2) ( 3, 6) y x y x 2248 2 2 4 6 8 (6, 3) (6, 8) 1 1 4 3 11234 y x (1, 2)(3, 2) x 1 2 1 3 4 2 1 3 4234 y ( ) 3 4 0, ( ) 1 2 7 2 , 1 1 2 1 2 3 1 5 4 1 4 () , 7 8 3 4 ( ) y x

Rates

NOT FOR SALE Section P.2Linear Models and Rat

16 Chapter PPreparation for Calculus © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 47. 3 30 x x 48. b m a 1 b yxb a b xyb a xy ab 49. 1 23 3260 xy xy 50. 1 2 2 3 3 1 22 32 320 xy xy xy xy 51. 1 12 1 3 1 33 xy aa aa a axy 30 xy 52. 1 34 1 1 1 11 xy aa aa a axy 10 xy 53. 1 2 92 1 2 94 1 2 52 5 2 xy aa aa a a a 55 22 1 2 2 1 55 25 250 xy xy xy xy 54. 2 3 1 2 1 2 2 3 4 3 xy aa aa a a 44 33 1 4 3 3340 xy xy xy 55. Thegivenlineisvertical. (a) 7, x or 70 x (b) 2, y or 20 y 56. Thegivenlineishorizontal. (a) 0 y (b) 1, x or 10 x 124 1 2 1 2 (3, 0) y x y x (0, b) (a, 0) paration parationCalculus Calc INSTRUCTORUSE

ONLY

Reserved.

753 834 24214030 040249

63. Theslopeis250. 1850when2. 25021850 2501350

Vt Vt t

64. Theslopeis4.50. 156when2.

Vt Vt t

4.52156

4.5147

65. Theslopeis1600. 17,200when2. 1600217,200

Vt Vt t

160020,400

66. Theslopeis5600. 245,000when2. 56002245,000

P.2

and

of Change 17 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 57. 2 2 1 xy yx m (a) 512 52 30 yx yx xy (b) 512 52 70 yx yx xy 58. 7 7 1 xy yx m (a) 213 23 10 yx yx xy (b) 213 23 05 yx yx xy 59. 3 2 423 2 2 xy yx m (a) 122 124 023 yx yx xy (b) 1 2 12 222 240 yx yx xy 60. 748 478 7 2 4 7 4 xy yx yx m (a) 175 246

2424 24124235 4224230 yx yx yx xy (b)

2442410 yx yx xy

5 3 5 3

yx m

yx yx xy

2440530 yx yx xy 62. 37 44 3 4 347 437 xy yx yx m (a) 3 4 3 4 54 53 420312 3480 yx yx yx xy

4 3 16 4 33 54 5 315416

yx yx yx xy

Section

Linear Models

Rates

1735

145 276 42212420

61.

530 xy

(a)

(b) 733 854 40352418

(b)

04331

5600256,200 Vt

NOT FOR SALE

10 1 21 202 213

67. 1 2 12

m m mm

Thepointsarenotcollinear.

6410 707 1147 505

71. Equationsofaltitudes: ab yxa c xb

68. 1 2 12

m m mm

Thepointsarenotcollinear.

69. Equationsofperpendicularbisectors: 22 22

cabab yx c cabba yx c

Settingtheright-handsidesofthetwoequationsequal andsolvingfor x yields 0. x Letting 0 x ineitherequationgivesthepointof intersection: 222 0,. 2 abc c

Thispointliesonthethirdperpendicularbisector, 0. x

72. Theslopeofthelinesegmentfrom , 33 bc to 22

70. Equationsofmedians: 3 3

c yx b c yxa ab c yxa ab

Solvingsimultaneously,thepointofintersectionis 33,. bc

18 Chapter PPreparation for Calculus

Rights

May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reserved.

ab b c

ab yxa c Solvingsimultaneously,thepointofintersectionis 22 ,.

ab b c is: 22 1 222 222 3 3 333 33 232 abcc m bb abccabc bbc Theslopeofthelinesegmentfrom , 33 bc to 222 0, 2 abc c is: 222 2 2222 222 12 23 03 33326 33 32 abccc m b abcccabc bbc mm Therefore,thepointsarecollinear. ( a, 0) (a, 0) (b, c) y x ab + 2 c 2 () , ba 2 c 2 () , ab + 2 c 2 () , ba 2 c 2 () , (0, 0) y x ( a, 0)(a, 0) (b, c) ( a, 0) (a, 0) (b, c) y x

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Section P.2Linear Models and Rat Sectione

73. 4 axby

(a) Thelineisparalleltothe x-axisif 0 a and 0. b

(b) Thelineisparalleltothe y-axisif 0 b and 0. a

584 54 xy yxx

5 11 882

(d)Theslopemustbe 5 2 Answerswillvary. Sample answer: 5 a and 2. b

524 542 xy yxx

5 1 22

(e) 5 2 a and 3. b

5 2 34 568 xy xy

12 So,0.0715,00020003050. WW

Whensalesexceed$15,000,thecurrentjobpaysmore.

78. (a)

74. (a) Lines c, d, e and f havepositiveslopes.

(b) Lines a and b havenegativeslopes.

(d) Lines b and f appearperpendicular. Lines b and d appearperpendicular.

75. Findtheequationofthelinethroughthepoints(0,32) and(100,212). 1809 1005

m FC FC or

320 32

9 5 9 5

1 9 5160 591600 CF FC For 72,22.2.FC

76. 0.51200 For137,0.51137200$269.87. Cx xC

1 2

Newjoboffer:0.052300 Ws Ws

0.02300 15,000 WW ss s s

77. (a)

Currentjob:0.072000

(b) Usingagraphingutility,thepointofintersectionis(15,000,3050).

Analytically, 0.0720000.052300

175675 3.86years x x x 0 0 6 1000 0 1500 3500 20,000 (15,000, 3050)

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79. (a) Twopointsare(50,780)and(47,825). Theslopeis 82578045 15. 47503 m 7801550 15750780151530 px pxx or 1 1530 15 x p

(b) If 855, p then 45 x units.

80. (a) 18.913.97 yx quizscore,testscorexy

(b)

(d) Theslopeshowstheaverageincreaseinexamscore foreachunitincreaseinquizscore.

(e) Thepointswouldshiftverticallyupward4units. Thenewregressionlinewouldhavea y-intercept 4greaterthanbefore: 22.913.97. yx

81. Thetangentlineisperpendiculartothelinejoiningthe point(5,12)andthecenter(0,0).

82. Thetangentlineisperpendiculartothelinejoiningthe point 4,3 andthecenterofthecircle,(1,1). Slopeofthelinejoining(1,1)and 4,3 is

Slopeofthelinejoining(5,12)and(0,0)is 12 5

2014

Learning.

20 Chapter PPreparation for Calculus

Cengage

Theequationofthetangentlineis 5 125 12 5169 1212 5121690. yx

134 143 Tangentline: 3 34 4 3 6 4 03424 yx yx xy 83. 20 xy 22 12112 11 552 2 2 d 84. 22 423310 7 43100 5 43 xyd 85. Apointontheline 1 xy is(0,1).Thedistance fromthepoint(0,1)to 50 xy is 22 10115 15 4 22. 22 11 d 86. Apointontheline

1,1 to 34100 xy is 2 2 314110 3410 9 55 34 d 0 0 1600 50 0 0 20 100 x y (5, 12) (0, 0) 4 4816 8 8 16 8 x y 2 624 2 6 2 4 (1, 1) (4, 3)

341 xy is 1,1.The distancefromthepoint

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Calculus 10th Edition Larson Solutions Manual

Calculus 10th Edition Larson Solutions Manual

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CHAPTER P PreparationforCalculus

Section P.1 Graphs and Models

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NOT FOR SALE P.1Graph Sections

NOT FOR SALE P.1Graphs

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NOT FOR SALE P.1Graphs

Section P.2 Linear Models and Rates of Change

Section P.2 Linear Models and Rate Rat INSTRUCTORUSE ONLY © Cengage Learning. All Rights Reserved.

Section P.2Linear Models and Rat Sectione

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