Chapter 2 Limits

2.1 The Idea of Limits

Figure 2.1

Figure 2.2 (a)

Figure 2.2 (b)

Figure 2.3

Table 2.1

Figure 2.4

Figure 2.5

Figure 2.6 (1 of 3)

Figure 2.6 (2 of 3)

Figure 2.6 (3 of 3)

2.2 Definitions of Limits

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Table 2.2

Figure 2.11 (a & b)

Figure 2.12 (a & b)

Table 2.3

Figure 2.13

Table 2.4

Figure 14

Techniques for Computing Limits 2.3 Techniques for Computing Limits

Figure 2.15

Figure 2.16

Figure 2.17

Figure 2.18

Figure 2.19 (a)

Figure 2.19 (b)

Table 2.5

Figure 2.20

Figure 2.21

Figure 2.22

2.4 Infinite Limits

Table 2.6

Table 2.7

Figure 2.23

Figure 2.24 (a)

Figure 2.24 (b)

Figure 2.25

Figure 2.26 (a & b) continued…

Figure 2.26 (c & d)

Figure 2.27

Table 2.8

Figure 2.28

Figure 2.29

2.5 Limits at Infinity

Figure 2.30

Figure 2.31

Figure 2.32

Figure 2.33

Figure 2.34

Figure 2.35

Figure 2.36

Figure 2.37

Figure 2.38

Figure 2.39

Figure 2.40

Figure 2.41

Figure 2.42

Figure 2.43

Figure 2.44

Figure 2.45

Table 2.9

2.6 Continuity

Figure 2.46 (a)

Figure 2.46 (b)

Figure 2.47

Figure 2.48

Identify discontinuities Example 2

Figure 2.49

Limit of a composition Example 4

Example 5 Limits of composite functions

Figure 2.50 (a)

Figure 2.50 (b)

Example 6 Intervals of continuity

Figure 2.51

Figure 2.52

Continuity of Trig Functions

Figure 2.53

Figure 2.54

Figure 2.55

Limits of Transcendental Functions Example 8

Figure 2.56

Figure 2.57

Figure 2.58

Precise Definitions of Limits 2.7 Precise Definitions of Limits

Figure 2.59

Figure 2.60 (a)

Figure 2.60 (b)

Figure 2.61 (a)

Figure 2.61 (b)

Figure 2.62

Figure 2.63

Figure 2.64

Figure 2.65

Figure 2.66

Figure 2.67 (a)

Figure 2.67 (b)

Figure 2.68 (a)

Figure 2.68 (b)

Figure 2.69