Existence of Limits

Figure 3.3.1 (a) shows a typical limit. Looking at the point (c, L) through an infinitesimal microscope, we can see the entire portion of the curve with x ≈ c because f(x) will be infinitely close to L and hence within the field of vision of the microscope.

Figure 3.3.1

In Figure 3.3.1 (b), part of the curve with x ≈ c is outside the field of vision of the microscope, and the limit does not exist.