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Chapter 2 | Limits
Figure 2.13 The graph of f ( x ) = (sin x )/ x confirms the estimate from Table 2.2 .
Example 2.5 Evaluating a Limit Using a Table of Functional Values 2
x −2
Evaluate lim x →4
using a table of functional values.
x −4
Solution As before, we use a table—in this case, Table 2.3 —to list the values of the function for the given values of x .
x −2
x −2
x
x
x −4
x −4
3.9
0.251582341869
4.1
0.248456731317
3.99
0.25015644562
4.01
0.24984394501
3.999
0.250015627
4.001
0.249984377
3.9999
0.250001563
4.0001
0.249998438
3.99999 0.25000016
4.00001 0.24999984
Table 2.3 Table of Functional Values for lim x →4
x −2
x −4
After inspecting this table, we see that the functional values less than 4 appear to be decreasing toward 0.25 whereas the functional values greater than 4 appear to be increasing toward 0.25. We conclude that
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