X2

Note that if x = 4, then the fraction collapses to the absurd expression "0/0." Thus, the function F is not defined for x = 4, but one can still ask what happens to F(x) when x is close to 4. Using a calculator (except when x = 4), we find the values shown in Table 4.1.

TABLE 4.1 Values of F(x) = (x2 - 16)/(4>/x - 8) when x is close to 4

F(x) 7.850 7.985 7.998 8.000 * 8.000 8.002 8.015 8.150

'Not defined.

It seems obvious from the table that as x gets closer and closer to 4, so the fraction F(x) gets closer and closer to 8. It therefore seems reasonable to say that

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F(x) tends to 8 in the limit as x tends to 4. We write x2- 16

8 as

In Fig. 4.11 we have drawn a portion of the graph of F. The function F is defined for all x > 0, except at x ā€” A. Also linw4 F(x) = 8. (A small circle is used to indicate that the corresponding point (4, 8) is not in the graph of F.)

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