Chapter 2 | Limits
139
x −2 x −4 =0.25.
We confirm this estimate using the graph of f ( x ) = x −2 x −4
lim x →4
shown in Figure 2.14 .
Figure 2.14 The graph of f ( x ) = x −2
x −4 confirms the
estimate from Table 2.3 .
Estimate lim x →1 1
2.4
x −1 x −1 using a table of functional values. Use a graph to confirm your estimate.
At this point, we see from Example 2.4 and Example 2.5 that it may be just as easy, if not easier, to estimate a limit of a function by inspecting its graph as it is to estimate the limit by using a table of functional values. In Example 2.6 , we evaluate a limit exclusively by looking at a graph rather than by using a table of functional values.
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