Infinite Limits vs. Limits That Do Not Exist

This example provides a graph and has us evaluate multiple one-sided and two-sided limits. We will see that all one-sided limits are infinite limits, which technically means that they do not exit since limit values must be in the real numbers. However, we will still write plus or minus infinity for these, since just stating “Does Not Exist” provides us with little information. On the other hand, when limits from different directions approach different infinities (positive vs. negative), we will definitively say that the limit does not exist.

Different classes and different textbooks will see this differently, so double check the context of your particular instance.

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