1. Chapter 3
The Derivative

2. Section 3.1
Limits

3. Figure 1

5. Figure 2

6. Figure 3 - 4

7. Figure 5

8. Figure 6

9. Figure 7

11. Figure 8

14. Your Turn 5
Suppose and Use the limit rules to find Solution:

15. Your Turn 6
Solution: Rule 4 cannot be used here, since The numerator also approaches 0 as x approaches −3, and 0/0 is meaningless. For x ≠ − 3 we can, however, simplify the function by rewriting the fraction as Now Rule 7 can be used.

16. Figure

17. Figure 11

18. Figure 12

19. Figure 13

21. Your Turn 8
Solution: Here, the highest power of x is x2, which is used to divide each term in the numerator and denominator.

23. Section 3.2
Continuity

24. Figure 14

26. Figure

27. Figure 17

28. Figure 18

29. Figure 19

33. Your Turn 1
Find all values x = a where the function is discontinuous. Solution: This root function is discontinuous wherever the radicand is negative. There is a discontinuity when 5x + 3 < 0

34. Your Turn 2
Find all values of x where the piecewise function is discontinuous. Solution: Since each piece of this function is a polynomial, the only x-values where f might be discontinuous here are 0 and 3. We investigate at x = 0 first. From the left, where x-values are less than 0, From the right, where x-values are greater than 0 Continued

35. Your Turn 2 Continued
Because the limit does not exist, so f is discontinuous at x = 0 regardless of the value of f(0). Now let us investigate at x = 3. Thus, f is continuous at x = 3.

36. Figure 20

37. Figure 21

38. Figure 22

39. Section 3.3
Rates of Change

41. Figure 23

42. Figure 24

44. Figure 25

46. Figure 26

47. Definition of the Derivative
Section 3.4
Definition of the Derivative

48. Figure 27

49. Figure 28

50. Figure 29

51. Figure 30

53. Figure 31

54. Figure 32

55. Figure

56. Figure 35

57. Figure

61. Figure 38

64. Figure 39

66. Figure 40

67. Figure

68. Figure 43

70. Figure 44

71. Graphical Differentiation
Section 3.5
Graphical Differentiation

72. Figure 45

73. Figure 46

74. Figure

75. Figure 49

76. Figure 50

77. Figure 51

78. Figure 52

79. Figure 53

80. Figure 54

81. Extended Application: A Model for Drugs Administered Intravenously
Chapter 3
Extended Application: A Model for
Drugs Administered Intravenously

82. Figure 55

83. Figure 56

84. Figure 57