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Chapter 2 | Limits
Example 2.6 Evaluating a Limit Using a Graph
For g ( x ) shown in Figure 2.15 , evaluate lim x →−1 g ( x ).
Figure 2.15 The graph of g ( x ) includes one value not on a smooth curve.
Solution Despite the fact that g (−1) =4, as the x -values approach −1 from either side, the g ( x ) values approach 3. Therefore, lim x →−1 g ( x ) =3. Note that we can determine this limit without even knowing the algebraic expression of the function.
Basedon Example 2.6 , we make the following observation: It is possible for the limit of a function to exist at a point, and for the function to be defined at this point, but the limit of the function and the value of the function at the point may be different.
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