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NOT FOR SALE, The Complete Solutions Manual for Calculus I with Precalculus A One Year Course Third Edition is a supplement. to the text by Ron Larson and Bruce H Edwards Solutions to every exercise in the text are given with all essential. algebraic steps included,INSTRUCTOR USE ONLY,Cengage Learning All Rights Reserved. Prerequisites,Section P 1 Solving Equations 2,Section P 2 Solving Inequalities 17. Section P 3 Graphical Representation of Data 36,Section P 4 Graphs of Equations 44. Section P 5 Linear Equations in Two Variables 55,Review Exercises 70.
Chapter Test 83,Problem Solving 85,INSTRUCTOR USE ONLY. 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,NOT FOR SALE,C H A P T E R P. Prerequisites,Section P 1 Solving Equations,1 equation 14 7x 2 23. 7x 2 2 23 2,3 extraneous 7x 21, 4 factoring extracting square roots completing the square. Quadratic Formula x 3, 5 4 x 1 4 x 4 is an identity by the Distributive 15 8x 5 3 x 20.
Property It is true for all real values at x 8 x 3x 5 3 x 3 x 20. 6 6 x 3 5 2 x 10 is conditional There are 5x 5 5 20 5. real values of x for which the equation is not true 5x 25. 7 4 x 1 2 x 4x 4 2x 2x 4 2 x 2 5x 25, This is an identity by simplification It is true for all real x 5. values of x,16 7x 3 3x 17,8 x 2 2 3x 2 x 2 6 x 4 is an identity by. 7 x 3 3 3x 3x 17 3 3 x, simplification It is true for all real values of x. 9 3 is conditional There are real,17 4 y 2 5 y 7 6y. values of x for which the equation is not true,5 3 2 y 6y 7 6y 6y.
10 24 is conditional There are real values of x, for which the equation is not true for example x 1. 2 2 5y 7 2,11 x 11 15 5y 5,x 11 11 15 11 5 5,12 7 x 19 18 3 x 3 5 1 x 1. 7 x x 19 x 3x 9 5 5x 1,7 19 x 3x 9 4 5x,7 19 19 x 19 3x 9 5 x 9 4 5x 5x 9. 13 7 2x 25 x 85,7 7 2x 25 7,19 x 3 2 x 3 8 5x,x 6x 9 8 5x. 2 2 5 x 9 8 5x,x 9 5 x 5 x 9 8 5x 5x,INSTRUCTOR USE ONLY.
No solution, 2 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,Chapter P 1 Solving. Solvin Equations,20 9 x 10 5 x 2 2 x 5 100 4 x 5x 6. 9 x 10 5 x 4 x 10 3 4,100 4 x 5x 6,9 x 10 9 x 10 12 12 12 6. The solution is the set of all real numbers,4 100 4 x 3 5 x 6 72.
3x 4x 400 16 x 15 x 18 72,24 24 4 x 10,9 x 32 x 96 17 y 32 y. 23 x 96 y y,23 23 17 y 32 y,23 17 y 32 y 100 y,x x 3x 49 2 y 100 y. 5 2 10 49 98 y,2x 5x 30 3 x 5x 4 2,6 x 30 5x 4 3,x 5 3 5 x 4 2 5 x 4. 15 x 12 10 x 8,4 32 z 5 1,4 z 5 4 z 24,6 z 5 z 24 0 x x. 6 z 30 z 24 0 15 6,24 0 60 x 0 40 100 x 50,0 60 x 40 0 40 x 50 x.
x 50 31 3 2,25 x 8 2 x 2 x 2,3 z 2 2 z 2,x 8 2x 4 x z 2. x 8 x 4 3z 6 2z 4 2,Contradiction no solution 1 2,32 0 Multiply both sides by x x 5. 26 8 x 2 3 2 x 1 2 x 5,1 x 5 2 x 0,8 x 16 6 x 3 2 x 10. 2 x 13 2 x 10,Contradiction no solution x,INSTRUCTOR USE ONLY. 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,4 Chapter P,NOT FOR SALE.
Prerequisites,requisites,33 2 0 Multiply both sides by x 4. x 4 2 x 4 0,x 4 2x 8 0, A check reveals that x 4 is an extraneous solution because it makes the denominator zero. There is no real solution,34 4 Multiply both sides by 2 x 1 2 x 1. 7 2 x 1 8 x 2 x 1 4 2 x 1 2 x 1,14 x 7 16 x 8 x 2,Multiply both sides by x x 3. x x 3 x x 3,3 4 x 12 x, A check reveals that x 3 is an extraneous solution because it makes the denominator zero.
There is no solution,36 Multiply both sides by x x 3. x x 3 x x 3,6 x 3 2 x 3 x 5,6 x 18 2 x 3 x 15,4 x 18 3 x 15. A check reveals that x 3 is an extraneous solution because it makes the denominator zero. There is no solution,39 2 x 2 3 8x,x2 4 x 4 5 x2 6x 9 General form 2 x 2 8 x 3 0. x 0 13 3 x 2 14 x 49 0,13 3 x 42 x 147,2 x 1 4 x 2 x 1. General form,4 x2 4x 1 4x2 4x 4,3 x 2 42 x 134 0,INSTRUCTOR USE ONLY.
This is a contradiction So the equation has no solution. 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,NOT FOR SALE Chapter P 1 Solving. Solvin Equations,5 3x 2 10 18 x 50 2x2 19 x 33,90 x 2 x 19 x 33. General form 3x 90 x 10 2,0 2 x 3 x 11 0,2x 3 0 x 32. 42 x x 2 5x2 1,x 11 0 x 11,x2 2x 5x2 1,4 x 2 2 x 1 0 51 x2 4x 12. 1 4 x 2 2 x 1 1 0 x 4 x 12,General form 4 x 2 2 x 1 0.
x 6 0 or x 2 0,0 x 6 or x 2,3x 2 x 1 0,52 1 x2 x 16 0. 3x 0 or 2 x 1 0 8,x 2 8 x 128 0,x 0 or x 12,x 16 x 8 0. 44 9x2 4 0 x 16 0 x 16,3 x 2 3 x 2 0 x 8 0 x 8,3x 2 0 or 3 x 2 0 53 x 2 2ax a 2 0. 45 x2 2x 8 0,x 4 0 or x 2 0 54 x a 2 b 2 0,x 4 or x 2 x a b. 46 x 2 10 x 9 0 x a b,x 9 x 1 0 x a b 0 x a b,x a b 0 x a b.
47 x 12 x 35,x 7 0 or x 5 0,x r 32 r4 2,x 7 or x 5. 57 3x 2 81,48 4 x 2 12 x 9 0 2,2 x 3 2 x 3 0,2x 3 0 x 32. 58 9 x 2 36,49 3 5x 2 x2 0 x 4,3 x 1 2 x 0 x r 4 r2. 3 x 0 or 1 2 x 0,x 3 or x 12,INSTRUCTOR USE ONLY, 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,6 Chapter P,NOT FOR SALE.
Prerequisites,requisites,x 12 r4 x 5 r x 4,x 5 x 4 or x 5. x 16 or x 8,5 z 4 or x 5 x 4,x 13 r5 The only solution to the equation is x 92. x 13 r 5 8 18,67 x 2 4 x 32 0,x 2 r 14 x 4x 2,x 2 r 14 x 2. x 4 or x 8,68 x2 6x 2 0,2x 1 r 18 x 6x 3,2x 1r3 2 x 3. 1r3 2 x 3 r 7,64 2 x 3 27,69 x 2 12 x 25 0,2x 3 r 27 x 12 x 6.
2x 3 r3 3 x 6,2x 3 r 3 3 x 6 r 11,3 r 3 3 x 6 r 11. 70 x 2 8 x 14 0,x 7 x 3 or x 7 x 3 x 4,7 z 3 or 2x 4. The only solution to the equation is x 2,INSTRUCTOR USE ONLY. 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,NOT FOR SALE Chapter P 1 Solving. Solvin Equations,71 8 4 x x2 0 75 5 x 2 15 x 7 0,x2 4 x 8 x 2 3x.
x 2 4 x 22 8 22 2 2,x 2 r 12 3,x 2r 2 3 2 20,72 9 x 2 12 x 14 x r. r 2 15 r 85,x 2 r 2 10,76 3x 2 9 x 5 0,73 2x2 5x 8 0. 2x2 5x 8 x 2 3x 0,x2 x 4 x 2 3x,x2 x 4 x 2 3x,2 4 4 2 3 2. 4 16 2 3 4,74 4 x 2 4 x 99 0 3 7,x2 x 99 2 2 3,x 2 x 12 99. x 12 9 r 21,INSTRUCTOR USE ONLY, 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part.
Cengage Learning All Rights Reserved,8 Chapter P,NOT FOR SALE. Prerequisites,requisites,77 2 x 2 x 1 0 82 6x 4 x2. b r b 2 4ac x2 6x 4 0,2a b r b 4ac,1 r 12 4 2 1 2a. 2 2 6 r 62 4 1 4,1 r 3 1 2 1,4 2 6 r 36 16,78 25 x 2 20 x 3 0. b r b 2 4ac 2,20 r 20 4 25 3,2 25 83 12 x 9 x 2 3,9 x 12 x 3.
20 r 400 300,50 b r b 2 4ac,20 r 10 3 1 2a,50 5 5 12 r 122 4 9 3. 79 2 2 x x2 0,x2 2x 2 12 r 6 7 2 7,b r b 2 4ac,2a 84 4 x 2 4 x 4 0. 2 r 2 4 1 2,2 r 2 3 2a,2 1 r 1 2 4 1 1,80 x 10 x 22. b r b 2 4ac,85 9 x 2 24 x 16 0,10 r 100 88,2 b r b 2 4ac. 10 r 2 3 2a,2 24 r 242 4 9 16,81 x 2 14 x 44 0,b r b 2 4ac 18.
14 r 142 4 1 44 3,INSTRUCTOR USE ONLY, 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,NOT FOR SALE Chapter P 1 Solving. Solvin Equations,86 16 x 2 40 x 5 0 87 28 x 49 x 2 4. 2 49 x 28 x 4,2a b r b 4ac,40 r 40 4 16 5,2 16 28 r 282 4 49 4. 40 r 1600 320 2 49,32 28 r 0 2,40 r 16 5 98 7,88 3x x 2 1 0.
b r b 2 4ac,3 r 32 4 1 1,3 r 13 3 13,89 8t 5 2t 2,2t 2 8t 5 0. b r b 2 4ac 8 r 82 4 2 5 8 r 2 6 6,2a 2 2 4 2,90 25h 2 80h 61 0 5. 92 x 14 8x,b r b 2 4ac 7,2a x 20 x 196 8x,80 r 802 4 25 61. 2 25 x 28 x 196 0,80 r 6400 6100 25 x 2 1372 x 9604 0. b r b 2 4ac,1372 r 1372 4 25 9604,1372 r 921 984,y 2 12 y 25 0 686 r 196 6.
b r b 2 4ac,2a 93 0 1x 2 0 2 x 0 5 0,12 r 12 4 1 25. 0 2 4 0 1 0 5,6r 11 0 2 r,x 1 449 3 449,INSTRUCTOR USE ONLY. 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,10 Chapter P Prerequisites. requisites, 94 0 005 x 2 0 101x 0 193 0 100 x 2 14 x 49 0 Extract square roots. 0 101 4 0 005 0 193,0 101 r x 7,101 x2 x 11,0 Complete the square.
0 101 r 0 006341,2 137 18 063,95 422 x 2 506 x 347 0 12. 506 4 422 347,x 1 687 0 488,102 3x 4 2 x 2 7 Quadratic Formula. 96 3 22 x 2 0 08 x 28 651 0,0 2 x 2 3x 11,b r b 2 4ac. x 3 r 3 4 2 11,0 08 r 0 08 2 4 3 22 28 651,2 3 22 3r 97. 0 08 r 369 031,2 995 2 971 3 97,97 x2 2 x 1 0 Complete the square.
103 4 x 2 2 x 4 2x 8 Factor,x 2 2 x 12 1 12,x 1 0 or x 1 0. 98 11x 33x,104 a 2 x2 b2 0 Factor,ax b ax b 0,x 0 or x 3 0 a. x ax b 0 x,81 Extract square roots,105 2 x 4 50 x 2 0. x 3 9 or x 3 9,x 6 or x 12 2 x 2 x 5 x 5 0,2 x2 0 or x 5 0 or x 5 0. x 0 or x 5 or x 5,INSTRUCTOR USE ONLY, 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part.
Cengage Learning All Rights Reserved,NOT FOR SALE Chapter P 1 Solving. Solvin Equations,106 20 x 3 125 x 0 107 x 4 81 0,5 x 4 x 25 2. 9 x 3 x 3 0,5 x 2 x 5 2 x 5 0 x 9,0 No real solution. 5x 0 x 0 x 3 0 x 3,2x 5 0 x 52 x 3 0 x 3,2x 5 0 x 5. 108 x 6 64 0,x 2 x 2 2 x 4 x 2 x 2 2 x 4 0,0 No real solution by the Quadratic Formula.
0 No real solution by the Quadratic Formula,109 x3 216 0. x 6 x 6 x 36,0 No real solution by the Quadratic Formula. 110 9 x 4 24 x3 16 x 2 0 111 x3 3x 2 x 3 0,x 9 x 24 x 16. 0 x x 3 x 3,x2 0 x 0 x 3 x 1 x 1 0,3x 4 0 x 4 x 3 0 x 3. 112 x3 2 x 2 3x 6 0,x x 2 3 x 2,x 2 x 2 3 0,x2 3 0 No real solution.
113 x4 x x3 1,x 4 x3 x 1 0,x 1 x 1 x 2 x 1 0,INSTRUCTOR USE ONLY. 0 No real solution by the Quadratic Formula, 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,12 Chapter P Prerequisites. requisites,NOT FOR SALE,114 x 4 2 x3 16 8 x 4 x3,x 4 2 x3 8 x 16 0. x x 2 8 x 2,x 2 x 2 2 x 4 x 2 0,0 No real solution by the Quadratic Formula.
115 x4 4x2 3 0 116 36t 4 29t 2 7 0,3 x 1 x 1 0 6t,x 3 0 x 3 7. x 3 0 x 3 6,x 1 0 x 1 7,t2 1 0 No real solution,117 x6 7 x3 8 0. x3 8 x3 1 0,x 2 x 2 2 x 4 x 1 x 2 x 1 0,0 No real solution by the Quadratic Formula. 0 No real solution by the Quadratic Formula,118 x 6 3x3 2 0. 2 x 2 2 x 1 x x 1,0 No real solution by the Quadratic Formula.
x2 x 1 0 No real solution by the Quadratic Formula. 119 2 x 10 0 121 x 10 4 0,2x 10 x 10 4,2x 100 x 10 16. 120 7 x 6 0 122 5 x 3 0,7 x 6 5 x 3,49 x 36 5 x 9,INSTRUCTOR USE ONLY. 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. Cengage Learning All Rights Reserved,NOT FOR SALE Section P 1 Solving. Solvi Equations 13,123 2x 5 3 0 130 x 3,2x 5 3 x 3. No solution,124 3 2x 2 0 131 x 3,3 2x 2 x 3 53 2,3 2x 4 x 3 r5 5.
2 x 1 x 3 r 5 5,x 2 x 22 8 or x 2 x 22 8,2x 513 x 6 x 5 0 1r 1 4 1 14. 513 x 6 or x 5 2 1,133 3x x 1 2 x 1,4x 3 8 x 1 12,3 x 2 x 1 0. 4 0 x 1 0 x 1,5x 2 0 x 2 extraneous,127 5 x 26 4 x 5. 5 x 26 x 4,4 x 2 x 1 6 x x 1,5 x 26 x 8 x 16,2 x 2 x x 1 3 x 1. x 2 13 x 42 0,x 6 x 7 2 x x 1 2 x 3 x 1,2 x x 1 5 x 3.
x 6 or x 7 0,128 x 5 2x 5,x 10 5x 3 0 x 3,INSTRUCTOR USE ONLY. 2012 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part. iii CONTENTS Chapter P Prerequisites 1 Chapter 1 Functions and Their Graphs