Calculus AP Edition 9th Edition Larson Solutions Manual

[Pages:102]Calculus AP Edition 9th Edition Larson Solutions Manual

NOT FOR SALE Full Download:

CHAPTER P Preparation for Calculus

Section P.1 Graphs and Models.................................................................................2 Section P.2 Linear Models and Rates of Change....................................................11 Section P.3 Functions and Their Graphs.................................................................23 Section P.4 Fitting Models to Data..........................................................................33 Review Exercises ..........................................................................................................35 Problem Solving ...........................................................................................................41

INSTRUCTOR USE ONLY ? 2010 Brooks/Cole, Cengage Learning ? Cengage Learning. All Rights Reserved.

This sample only, Download all chapters at:

NOT FOR SALE

CHAPTER P Preparation for Calculus

Section P.1 Graphs and Models

1. y

3 2

x

3

x-intercept: (2, 0)

y-intercept: (0, 3)

Matches graph (b).

2. y

9 x2

x-intercepts: 3, 0, 3, 0

y-intercept: (0, 3) Matches graph (d).

3. y 3 x2

  x-intercepts: 3, 0 , 3, 0

y-intercept: (0, 3) Matches graph (a).

4. y x3 x

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

y-intercept: (0, 0) Matches graph (c).

5. y

1 2

x

2

x 4 2 0 2 4

y0 1 234

7. y 4 x2 x 3 2 0 2 3 y 5 0 4 0 5

y

6 (0, 4)

2 (- 2, 0) -6 -4

-2

(- 3, - 5) -4 -6

(2, 0) x

46

(3, - 5)

8. y x 32

x01234 5 6 y94101 4 9

y

10 (0, 9)

8

(6, 9)

6

4 2

-6 -4 -2 -2

(1, 4) (5, 4) (2, 1)

(4, 1) x

246 (3, 0)

9. y x 2

y

6

4

(0, 2) (-2, 1)

(4, 4) (2, 3)

-4 -2 (- 4, 0) -2

x 24

6. y 5 2x

x

1

0 1 2

5 2

3

4

y 7 5 3 1 0 1 3

x 5 4 3 2 1 0 1 y3 2 1 0 1 2 3

y

6

(- 5, 3)

4

(1, 3)

(- 4, 2) 2 (0, 2)

(- 3, 1) -6 -4 (- 2, 0)

(- 1, 1) x

2

-2

y

8 (-1, 7)

(0, 5)

4

(1, 3)

2

(2, 1)

x

(

INSTRUCTOR -6 -4 -2

(3, - 1)

( - 2

-4

5, 0 2

(4, -3)

USE

ONLY

2

? 2010 Brooks/Cole, Cengage Learning

? Cengage Learning. All Rights Reserved.

NOT FOR SALE Section P.1 Graphs and Models 3

10. y x 1

x 3 2 1 0 1 2 3 y 2 1 0 1 0 1 2

y

4 3 (- 3, 2) 2 (- 2, 1)

-3 -2 (- 1, 0) -1

-2

(3, 2)

(2, 1)

x 1 23

(1, 0) (0, - 1)

14. y

1

x 2

x 6 4 3 2

1 0 2

y

1 4

1 2

1

y

5

( ) 4

3

0,

1 2

( ) (-1, 1) 2

2,

1 4

x

( ) -

6,

-

1 4

-1 -2

( ) -

4,

-

1 2

-3

(- 3, - 1) -4

-5

123

Undef. 1

1

1

2

4

11. y x 6 x 0 1 4 9 16 y 6 5 4 3 2

y

2

x

-4

4 8 12 16

-2

(9, -3) (16, -2)

-4

(4, -4)

(1, -5) -6 (0, - 6)

-8

12. y x 2

x 2 1 0

2 7 14

y0 1

2 23 4

15. Xmin 5 Xmax 4 Xscl 1 Ymin 5 Ymax 8 Yscl 1

Note that y 3 when x 0 and y 0 when x 1.

16. Xmin 20 Xmax 30 Xscl 5 Ymin 10 Ymax 40 Yscl 5

Note that y 16 when x 0 or 16.

y

5

4

(14, 4)

3 (- 1, 1)

2

(7, 3) (2, 2)

(0, 2 )

(- 2, 0)

x 5 10 15 20

13. y 3 x

x 3 2 1 0

12 3

y 1

3 2

3 Undef. 3

3 2

1

17. y 5 x

5 (-4.00, 3)

(2, 1.73)

-6

6

-3

(a) 2, y 2, 1.73 y

(b) x, 3 4, 3 3

5 2

 5 4

 3 | 1.73

18. y x5 5x

6

(-0.5, 2.47)

y

-9

9

( (

3 2 (- 3, - 1) 1

-3 -2 -1 -1 -2

(1, 3)

(2,

3 2

(3, 1)

x 123

(-

2,

-

3 2

(1, -4)

-6

(a) 0.5, y 0.5, 2.47 (b) x, 4 1.65, 4 and x, 4

1, 4

INSTRUCTOR (-1,-3) USE ONLY

? 2010 Brooks/Cole, Cengage Learning

? Cengage Learning. All Rights Reserved.

NOT FOR SALE 4 Chapter P Preparation for Calculus

19. y 2x 5 y-intercept: y x-intercept: 0 5 x

20 5

2x 5

2x

 5

2

;

5 2

,

0

5; 0, 5

20. y 4x2 3 y-intercept: y

402 3

3; 0, 3

x-intercept: 0 4x2 3 3 4x2

None. y cannot equal 0.

21. y x2 x 2

y-intercept: y 02 0 2

y 2; 0, 2

x-intercepts: 0 0 x

x2 x 2

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

22. y2 x3 4x y-intercept: y2 y

03 40 0; 0, 0

x-intercepts: 0 0 x

x3 4x

xx 2x 2 0, r 2; 0, 0, r 2, 0

23. y x 16 x2 y-intercept: y 0 16 02

0; 0, 0

x-intercepts: 0 0 x

x 16 x2

x 4 x4 x 0, 4, 4; 0, 0, 4, 0, 4, 0

24. y x 1 x2 1

y-intercept: y 0 1 02 1 y 1; 0, 1

x-intercept: 0 x 1 x2 1 x 1; 1, 0

25. y 2 x 5x

y-intercept: None. x cannot equal 0.

x-intercept: 0

0 x

2 x 5x

2 x

4; 4, 0

x2 3x

26. y 3x 12

y-intercept: y y

02 30 ??30 1??2 0; 0, 0

x-intercepts: 0 0 x

x2 3x

3x 12

xx 3 3x 12

0, 3; 0, 0, 3, 0

27. x2 y x2 4 y 0

y-intercept: 02 y 02 4 y

y

0

0; 0, 0

x-intercept: x20 x2 40 0 x 0; 0, 0

28. y 2x x2 1

y-intercept: y 20 02 1 y 1; 0, 1

x-intercept: 0 2x x2 1

2x

x2 1

4x2 x2 1

3x2 1

x2 1 3

x r3 3

x

3 3

;

? ???

3 3

,

? 0???

Note: x 3 3 is an extraneous solution.

29. Symmetric with respect to the y-axis because

y x2 6 x2 6.

INSTRUCTOR USE ONLY ? 2010 Brooks/Cole, Cengage Learning ? Cengage Learning. All Rights Reserved.

NOT FOR SALE Section P.1 Graphs and Models 5

30. y x2 x No symmetry with respect to either axis or the origin.

31. Symmetric with respect to the x-axis because

y2 y2 x3 8x.

41. y 2 3x

 Intercepts: 0, 2,

2 3

,

0

Symmetry: None

y

32. Symmetric with respect to the origin because

y x3 x

y x3 x y x3 x.

2 (0, 2)

1

(2 3

,

0

(

x

-1

23

-1

33. Symmetric with respect to the origin because

x y xy 4.

34. Symmetric with respect to the x-axis because

x y2 xy2 10.

35. y 4 x 3 No symmetry with respect to either axis or the origin.

36. Symmetric with respect to the origin because

x y 4 x2 0

xy 4 x2 0.

37. Symmetric with respect to the origin because

y

x

x2 1

x

y

x2

. 1

x2

38. y

is symmetric with respect to the y-axis

x2 1

because y

x2 x2 1

x2

x2

. 1

39. y x3 x is symmetric with respect to the y-axis

 because y x3 x x3 x x3 x .

40. y x 3 is symmetric with respect to the x-axis because y x 3 y x 3.

42. y

3 2

x

6

Intercepts: 0, 6, 4, 0

Symmetry: None

y

8 6 (0, 6)

4

2

-2 -2

(4, 0) x

2468

43. y

1 2

x

4

Intercepts: 8, 0, 0, 4

Symmetry: none

y

2

-2 -2

(8, 0)

x

24

8 10

(0, - 4) -6 -8 - 10

44. y

2 3

x

1

 Intercepts: 0, 1,

3 2

,

0

Symmetry: none

y

2

( ) 3 2

,

0

-1

(0, 1)

x 12

-1

-2

INSTRUCTOR USE ONLY ? 2010 Brooks/Cole, Cengage Learning ? Cengage Learning. All Rights Reserved.

NOT FOR SALE 6 Chapter P Preparation for Calculus

45. y 9 x2

Intercepts: 0, 9, 3, 0, 3, 0

Symmetry: y-axis

y

10 (0, 9)

6

4

2 (-3, 0) -6 -4 -2

-2

(3, 0) x

246

49. y x3 2

 Intercepts: 3 2, 0 , 0, 2

Symmetry: none

y

5 4 3

(0, 2)

(- 3 2, 0) 1

-3 -2 -1

x 123

46. y x2 3 Intercept: (0, 3) Symmetry: y-axis

y

12

9

-6 -3

(0, 3)

x

3

6

47. y x 32

Intercepts: 3, 0, 0, 9

Symmetry: none

y

12 10

(0, 9) 8

2 -10 -8 -6 (- 3, 0)

-2

x 24

48. y 2x2 x x2x 1

 Intercepts: 0, 0,

1 2

,

0

Symmetry: none

y

5

4

3

2

( ) -

1 2

,

0

1

(0, 0)

-3 -2 -1

x 123

50. y x3 4x

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

Symmetry: origin

y

3

(-2, 0)

(0, 0) (2, 0)

x

-3

-1

1

3

-1

-2

-3

51. y x x 5

Intercepts: 0, 0, 5, 0

Symmetry: none

y

3 2

(- 5, 0)

(0, 0)

x

-4 -3 -2 -1

12

-3 -4

52. y

25 x2

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

Symmetry: y-axis

y

7 6 (0, 5)

4

3

2

(- 5, 0) 1

(5, 0)

x

-4-3-2-1 1 2 3 4 5

-2 -3

INSTRUCTOR USE ONLY ? 2010 Brooks/Cole, Cengage Learning ? Cengage Learning. All Rights Reserved.

NOT FOR SALE Section P.1 Graphs and Models 7

53. x y3

Intercept: (0, 0) Symmetry: origin

y

4 3 2

(0, 0)

x

-4 -3 -2 -1

1234

-2 -3 -4

54. x y2 4

Intercepts: 0, 2, 0, 2, 4, 0

Symmetry: x-axis

y

3

(-4, 0) -5

(0, 2)

-2 -1

x 1

(0, -2)

-3

55. y 8 x

Intercepts: none

Symmetry: origin

y

8

6

4

2

x

-2

2468

10 56. y x2 1

Intercept: (0, 10) Symmetry: y-axis

y

12 10 (0, 10)

2 -6 -4 -2

x 246

57. y 6 x

Intercepts: 0, 6, 6, 0, 6, 0

Symmetry: y-axis

y

8

6

4

(-6, 0)

2

-8

-4 -2-2

-4

-6

-8

(0, 6) 24

(6, 0) x

68

58. y 6 x Intercepts: (0, 6), (6, 0) Symmetry: none

y

8 (0, 6)

4

2 (6, 0)

x 2468

59. y2 x 9 y2 x 9 y r x9

Intercepts: 0, 3, 0, 3, 9, 0

Symmetry: x-axis

4 (0, 3)

(- 9, 0)

- 11

1

(0, -3) -4

60. x2 4 y2 4 y r 4 x2 2

Intercepts: 2, 0, 2, 0, 0, 1, 0, 1

Symmetry: origin and both axes

Domain: >2, 2@

(-2, 0) -3

2

(0, 1) (2, 0)

3

(0, -1) -2

INSTRUCTOR USE ONLY ? 2010 Brooks/Cole, Cengage Learning ? Cengage Learning. All Rights Reserved.

8 Chapter P Preparation for Calculus

61. x 3y2 6 3y2 6 x y r 6x 3

  Intercepts: 6, 0, 0, 2 , 0, 2

Symmetry: x-axis

3

(0, 2 )

(6, 0)

-1

8

(0, - 2 )

-3

62. 3x 4 y2 4y2

8 3x 8

y

r

3 4

x

2

 Intercept:

8 3

,

0

Symmetry: x-axis

6

( ) 8 , 0 3

-6

12

65. x2 y x y 6 x2 0 0 x

6 y 6 x2 4 y 4x 4 x x2 x 2

x 2x 1

2, 1

The corresponding y-values are y 2 for x y 5 for x 1.

Points of intersection: 2, 2, 1, 5

2 and

66. x y

3 x 3 x

0 x

3 y2 y2 3 x x 1

x 12

x2 2x 1

x2 x 2 x 1x 2

1 or x 2

The corresponding y-values are y 2 for x 1 and y 1 for x 2.

Points of intersection: 1, 2, 2, 1

-6

63. x y 8 y 8 x 4x y 7 y 4x 7 8 x 4x 7 15 5x 3x The corresponding y-value is y 5. Point of intersection: (3, 5)

67. x2 y2 5 y2 5 x2 x y 1 y x 1

5 x2 x 12

5 x2 x2 2x 1

0 2x2 2x 4 2x 1x 2

x 1 or x 2

The corresponding y-values are y 2 for x 1 and y 1 for x 2.

64. 3x 2 y 4x 2y

4 y 10 y

3x 4 2

4x 10 2

3x 4 2

3x 4

4x 10 2

4x 10

7x 14

x 2

The corresponding y-value is y 1.

Point of intersection: 2, 1

Points of intersection: 1, 2, 2, 1

68. x2 y2 25 y2 25 x2 3x y 15 y 3x 15

25 x2 3x 152

25 x2 9x2 90x 225 0 10x2 90x 200 0 x2 9x 20

0 x 5x 4

x 4 or x 5

The corresponding y-values are y 3 for x 4 and y 0 for x 5.

Points of intersection: 4, 3, 5, 0

INSTRUCTOR USE ONLY ? 2010 Brooks/Cole, Cengage Learning ? Cengage Learning. All Rights Reserved.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download