WIXLIB

Calculus AP Edition 9th Edition Larson Solutions ManualFull Download: tion-9th-edition-larson-solutions-manual/NOT FOR SALECHAPTER PPreparation for CalculusSection P.1Graphs and Models.2Section P.2Linear Models and Rates of Change.11Section P.3Functions and Their Graphs.23Section P.4Fitting Models to Data.33Review Exercises .35Problem Solving .41INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.This sample only, Download all chapters at: alibabadownload.com

NOT FOR SALEC H A P T E R PPreparation for CalculusSection P.1 Graphs and Models1. y 32 x 34 x27. yx-intercept: (2, 0)y-intercept: (0, 3)Matches graph (b).x 3 2023y 5040 5y9 x22. y6(0, 4)x-intercepts: 3, 0 , 3, 02( 2, 0)y-intercept: (0, 3) 6Matches graph (d).(2, 0)x 44( 3, 5)3. y6 2(3, 5) 43 x2 63, 0 , 3, 0x-intercepts:8. y2x 3y-intercept: (0, 3)Matches graph (a).x0123456x3 xy94101494. yx-intercepts: 0, 0 , 1, 0 , 1, 0y10y-intercept: (0, 0)8Matches graph (c).6(0, 9)45. y 21x22(6, 9)(5, 4)(1, 4)(2, 1)(4, 1)x 6x 4 2024y012349. yy6(4, 4)4 4 2 2426(3, 0)x 2x 5 4 3 2 101y3210123(2, 3)(0, 2)y( 2, 1)6x 4 2( 4, 0)24 24( 5, 3)( 4, 2) 26. y5 2x( 1, 1)( 3, 1) 6x 101252y7531034 1 3 4(1, 3)(0, 2)x( 2, 0)2 2y8( 1, 7)(0, 5)42(1, 3)(2, 1)INSTRUCTORSTUSE ONLY 66 44 22 22 44( (5,02(3, 1)x(4,(4 3)3) 2010 Brooks/Cole, Cengage Learning2 Cengage Learning. All Rights Reserved.

NOT FOR SALESection P.1x 110. y 3 2 10123y210 1012x 6 4 3 2 1y 14 12 1Undef.1y54323(3, 2)2( 2, 1)1 1( 1, 0)( 1, 1)215.x014916y 6 5 4 3 22812(9, 3)160 and y0 when(16, 2) 4(4, 4)(1, 5) 6(0, 6)16.Xmin 20Xmax30Xscl 5Ymin 10Ymax40Yscl 5 8x 212. y 3 when xNote that y 1.xx41 2 3Xmin 5Xmax4Xscl 1Ymin 5Ymax8Yscl 1y 214 2 3 4 5( 3, 1)x 6 412x 1( 6, 14 )( 4, 12 )3(1, 0)(0, 1) 211. y2(0, 12 )(2, 14 )(2, 1)x 3 20y4( 3, 2)31x 214. yxGraphs and ModelsGraphx 2 1y0102271423416 when xNote that yy17. y0 or 16.5 x554(14, 4)3( 4.00, 3)(2, 1.73)(7, 3)( 1, 1) 6(2, 2)(0, 2 )26 3x( 2, 0)13. y51015203xx 3 2 10123y 1 32 3Undef.3321y(a)2, y2, 1.73(b)x, 3 4, 318. y(2, 32 (x 29(1, 4)1 3 2 1 112( 2, 32 (5 46 6(3, 1)( 3, 1)3 1.73( 0.5, 2.47) 9235 2x5 5 x(1, 3)3y(a) 0.5, y(b)x, 4 0.5, 2.473 1.65, 4 and x, 41, 4INSTRUCTORSUSE ONLY( 1,( 1,1, 3) 3)) 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

4NOT FOR SALEChapter PPreparationparation for CalcCalculus2x 519. y2 x5x20 5x-intercept: 02x 5y-intercept: None. x cannot equal 0.52xx-intercept: 0x5;25,2 5; 0, 525. yy-intercept: y04x2 320. yy-intercept: y402 33; 0, 326. y4 x2 3x-intercept: 0 34 x22 x5x02 x4; 4, 0x 2 3x23x 102 3 0y-intercept: yª 3 0 1º¼None. y cannot equal 0.02 0 2y-intercept: yx 4xy0; 0, 0x-intercepts: 0x3 4 x24. y0, r 2; 0, 0 , r 2, 028. y2x 0 16 0220 x-intercept:x 16 x 2x0, 4, 4; 0, 0 , 4, 0 , 4, 00x2 13x 21x213xr02 1 1; 0, 1x1; 1, 0xx2 1 Note: x0; 0, 002 1x2 1x2 14x2x2 1x 12x 2x4 x 4 xxx-intercept: 00 1; 0, 1y0; 0, 00y0; 0, 0x2 1y-intercept: yx 16 x 20 10xxy-intercept: y0x-intercept: x 2 0 x 2 4 0x x 2 x 2x 10, 3; 0, 0 , 3, 0y0x-intercepts: 02y-intercept: 02 y 02 4 y03 4 0y-intercept: y 2y-intercept: y3x 127. x 2 y x 2 4 y32x x 3x 2, 1; 2, 0 , 1, 0x23. y3x 10x 2 x 102x 2 3xx-intercepts: 0x2 x 2x-intercepts: 020; 0, 0 2; 0, 2y22. yyx2 x 221. yx333 § 3; ,3 3·0 ¹3 3 is an extraneous solution.29. Symmetric with respect to the y-axis becausey x2 6x 2 6.INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

NOT FOR SALESection P.1x2 x30. y31. Symmetric with respect to the x-axis because y23 x yy(0, 2)2 x1 x x( 23 , 0(3 1x2x3 x.y0Symmetry: None32. Symmetric with respect to the origin because y2,3Intercepts: 0, 2 ,x3 8 x.y252 3x41. yNo symmetry with respect to either axis or the origin.Graphs and ModelsGraph3 133. Symmetric with respect to the origin because x yxy4. 32 x 642. yIntercepts: 0, 6 , 4, 034. Symmetric with respect to the x-axis becausex y24 35. ySymmetry: None 10.xy 2y8x 36No symmetry with respect to either axis or the origin.236. Symmetric with respect to the origin because x y 4 xxy 24 x2(4, 0) 200. 42(8, 0)x 2 2x2is symmetric with respect to the y-axisx 1 x x22 1x2.2x 1x x is symmetric with respect to the y-axis3 x x3 x4810(0, 4) 8 103 x2 62because yx8y44. y39. y6Symmetry: none 1because y4Intercepts: 8, 0 , 0, 4x.x2 1y38. y21x243. y x x2 237. Symmetric with respect to the origin because y(0, 6)4x3 x .2x3 1Intercepts: 0, 1 , 32 , 0Symmetry: noney40. y x3 is symmetric with respect to the x-axis2because y x3y x3.(0, 1)( 32 , 0)x 112 1 2INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

6NOT FOR SALEChapter PPreparationparation for CalculusCalc9 x245. yx3 249. yIntercepts: 0, 9 , 3, 0 , 3, 0Intercepts: 3 2, 0 , 0, 2Symmetry: y-axisSymmetry: noney10y(0, 9)54634(0, 2)2( 3, 0) 6 4 2(3, 0)x2 246x 3 2x2 346. y1( 3 2, 0)23x3 4 x50. yIntercept: (0, 3)1 1Intercepts: 0, 0 , 2, 0 , 2, 0Symmetry: y-axisSymmetry: originyy1239( 2, 0)(0, 0) 3 1(0, 3)3x3 362x 347. y 1 2x 3 6(2, 0)151. yx 5xIntercepts: 3, 0 , 0, 9Intercepts: 0, 0 , 5, 0Symmetry: noneSymmetry: noneyy1231082(0, 9)( 5, 0)(0, 0)x 4 3 2 1122 10 8 6x( 3, 0) 222x2 x48. y 34 4x 2x 1Intercepts: 0, 0 , 12 ,0Symmetry: none52. y25 x 2Intercepts: 0, 5 , 5, 0 , 5, 0Symmetry: y-axisyy576432( 12 , 0)1( 5, 0)(0, 0)x 3 2 11234321(0, 5)(5, 0)x 4 3 2 11 2 3 4 5 2 3INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

NOT FOR SALESection P.153. xy3Graphs and ModelsGraph76 x57. yIntercepts: 0, 6 , 6, 0 , 6, 0Intercept: (0, 0)Symmetry: originSymmetry: y-axisyy43826(0, 0)4x 4 3 2 11232( 6, 0)4(0, 6)(6, 0)x 8 2 4 2 2 3 4 4 64268 854. xy2 4Intercepts: 0, 2 , 0, 2 , 4, 058. y6 xIntercepts: (0, 6), (6, 0)Symmetry: x-axisSymmetry: noneyy38(0, 2)(0, 6)( 4, 0) 5 2x 114(0, 2)2(6, 0) 3x255. y8x59. y 2 xy2Intercepts: noneySymmetry: origin4689x 9rx 9Intercepts: 0, 3 , 0, 3 , 9, 0y8Symmetry: x-axis644(0, 3)2x 2246( 9, 0)8 111(0, 3) 456. y10x2 160. x 2 4 y 2Symmetry: y-axis4 x22Symmetry: origin and both axesyDomain: 2, 2@12(0, 10)2(0, 1)( 2, 0) 3(2, 0)32 6 4 2rIntercepts: 2, 0 , 2, 0 , 0, 1 , 0, 1Intercept: (0, 10)104 y(0, 1)x246 2INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

Chapter P861. x 3 y 2Preparationparation for CalculusCalc665. x 2 y6 y6 x2x y4 y4 x6 x3y26 x6 x3ry2 , 0, Intercepts: 6, 0 , 0,4 x0x2 x 2x 2 x 1022, 1xSymmetry: x-axisThe corresponding y-values are y3( 0,2)y8( 0, 366.8ry8,3Intercept:3x43 y2 y2yx 10( 83 , 0)0x2 x 2x 1 or xx y8 y8 x4x y7 y4x 7x y5 x25 x4x 75xxThe corresponding y-value is y5.Point of intersection: (3, 5)4x 2 y3x 423x 421 for x67. x 2 y 2 664. 3x 2 yx 1 x 2 4 y 10 y 2 for x 12.Points of intersection: 1, 2 , 2, 11232x2 2x 1and y 63 xThe corresponding y-values are y615x 13 x 2Symmetry: x-axis8 xx3 x3x 84 y22 andPoints of intersection: 2, 2 , 1, 52)62. 3x 4 y 22 for x 1 .5 for x(6, 0) 163.2 4 x 102 4 x 105 x21 yx 1x 122x2 2x 102x2 2 x 4x 1 or x2 x 1 x 22The corresponding y-values are y1 for xand y3x 42 4 x 1025 y2 12.Points of intersection: 1, 2 , 2, 168. x 2 y 2 3 x y25 y 225 x 215 y3 x 153x 15225 x225 x29 x 2 90 x 2257x 14010 x 2 90 x 200x 20x 2 9 x 200x 5 x 4The corresponding y-value is y 2 for x 1.xPoint of intersection: 2, 1 4 or x 5The corresponding y-values are yand y0 for x3 for x 4 5 .Points of intersection: 4, 3 , 5, 0INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

NOT FOR SALESection P.1GraphsGraph and Models72. Analytically,yx3yxyx4 2 x2 1x3xy1 x2x3 x01 x269.x x 1 x 1x0 1, or x0, x1The corresponding y-values are 1 for xy0 for x0, yy91 for x 1 , andx4 2 x2 10x4 x20x2 x 1 x 1x 1, 0, 1.Points of intersection: 1, 0 , 0, 1 , 1, 01.y x 4 2x 2 12Points of intersection: 0, 0 , 1, 1 , 1, 1(0, 1)yx 4xy x 2x 4x x 270.3x3 3x 2x 1x2 33 x2 4 xy 2y 1 x2x 673. y03(1, 0) 20x 21 or x( 1, 0)4The corresponding y-values arey 3 for x 1 and y0 for xy x 6(3, 2 .Points of intersection: 1, 3 , 2, 03)( 2, 2) 72 x 2 4xy 271. Analytically,Points of intersection: 2, 2 , 3,yx3 2 x 2 x 1y x 2 3x 1x3 2 x 2 x 1 x 2 3x 1x3 x 2 2 x0x x 2 x 10xx 6x2 5x 6x 3 x 2x 1, 0, 2.Points of intersection: 1, 5 , 0, 1 , 2, 14x 6Analytically,y x3 2x2 x 174. yy3 3, 1.732 x2 4x x2 4 x00 3, 2. 2x 3 66 x7 4(2, 1)(0, 1)6y 6 x(1, 5)( 1, 5)(3, 3) 8 48y x2 3x 1 1y 2x 3 6Points of intersection: (3, 3), (1, 5)Analytically, 2 x 3 62x 32x 3xx or 2 x 33 orx6 xx x1.INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

10NOT FOR SALEChapter PPreparationparation for CalculusCalc75. (a) Using a graphing utility, you obtain 0.027t 5.73t 26.9.y(b)76. (a) Using a graphing utility, you obtain2y(b)250 50.77t 2 2.1t 424035180 500The model is a good fit for the data.(c) For 2010, t40 and y212.9.C77.5.5 x 10,0005.5 x0(c) For 2015, t25 and y 538 million subscribers.R3.29 x230.25 xThe model is a good fit for the data.3.29 x 10,000210.8241x 2 65,800 x 100,000,00010.8241x 2 65,830.25 x 100,000,000 Use the Quadratic Formula.x 3133 unitsThe other root, x 2949, does not satisfy the equation RC.This problem can also be solved by using a graphing utility and finding the intersection of the graphs of C and R.78. y81. (a) If (x, y) is on the graph, then so is x, y by y-axis10,770 0.37x2symmetry. Because x, y is on the graph, then so400is x, y by x-axis symmetry. So, the graph is0symmetric with respect to the origin. The converse isx3 has origin symmetrynot true. For example, ybut is not symmetric with respect to either the x-axisor the y-axis.1000If the diameter is doubled, the resistance is changed byapproximately a factor of 14 . For instance,(b) Assume that the graph has x-axis and originsymmetry. If (x, y) is on the graph, so is x, y byx-axis symmetry. Because x, y is on the graph,y 20 26.555 and y 40 6.36125.then so is x, y79. Answers may vary. Sample answer:yxsymmetry. Therefore, the graph is symmetric withrespect to the y-axis. The argument is similar fory-axis and origin symmetry.x 4 x 3 x 8 has intercepts at 4, x3, and x x, y by origin8.80. Answers may vary. Sample answer:yx x 32 , x32x 4 x has intercepts at5.24, and x82. (a) v ªBecause y 523 x(b) i ª Because y2 33x3 3x3 x 2 3º¼3 x x 1 x 1 has x-intercepts 0, 0 , 1, 0 , 1, 0 º¼(c) None of the equations are symmetric with respect to the x-axis(d) ii ªBecause 2 3 2(e) i ªBecause 3 x 3i ªBecause 3 0(f)( 303 3 x1º and vi ª Because¼ 3 x 3 3 x 2 31º¼ yº and iv ª Because¼0º and iv ª Because¼3 x 3 x yº¼0º¼INSTRUCTOR USE ONLY30 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.

NOT FOR SALESection P.283. False. x-axis symmetry means that if 4, 5 is on theLinear Models and RateRates of Changey87.4graph, then 4, 5 is also on the graph. For example,4, 5 is not on the graph of x(0, 3)y 2 29, whereas2 4, 5 is on the graph.(x, y)1 2x 1f 4 .84. True. f 411(0, 0)23 1§ b r85. True. The x-intercepts are § b86. True. The x-intercept is , 2ab 2 4ac,2a·0 . ¹x 02·0 .¹2 y 32x 024ª x 2 y 3 º ¼x2 y 24 x 2 4 y 2 24 y 36x2 y 23 x 2 3 y 2 24 y 360x y 8 y 12022x y 4222 y 024Circle of radius 2 and center (0, 4).88. Distance from the originx2 y 2K u Distance from 2, 0Kx2 y 2x 22 y2 , K z 1K 2 x2 4 x 4 y21 K 2 x2 1 K 2 y 2 4K 2 x 4K 20Note: This is the equation of a circle!Section P.2 Linear Models and Rates of Change1. m1y8.m 32. m23. m04. m 11m 3( 2, 5)6m 04m 3x 6 224 25. m 126. m4032 45 39. m623y7.m 2y3m is undefined.(5, 2)x 1m 18(3, 4)423567 3 42x 21 26 6 421m 32248 10(3, 4) 5INSTRUCTOR USE ONLY 2010 Brooks/Cole, Cengage Learning Cengage Learning. All Rights Reserved.