Precalculus: A Functional Approach to Graphing and Problem Solving, 6th Edition

Figure 2.40 Limit as x → c

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 ...