Limits by Graphing or by Table

Figure 2.40 shows the graph of a function f and the number *c* = 3.

The arrowheads are used to illustrate possible sequences of numbers along the x-axis, approaching from both the left and the right. As *x* approaches *c* = 3, *f(x*) gets closer and closer to 5. We write this as

As *x* approaches 3 from the left, we write *x* → 3^{-}, and as *x* approaches 3 from the right, we write *x* → 3^{+}. We say that the limit at *x* = 3 exists only if the value approached from the left is the same as the value approached ...

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