Figure 2.40 Limit as xc

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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