One-Sided Limits

A one-sided limit describes how a function behaves as the input approaches a particular value from only one direction—either from values smaller than that number or from values larger than it. Instead of looking at what happens exactly at the point, we observe how the function’s outputs behave as we move closer and closer from one side. This idea is especially important when a function changes behavior at a point, such as when there is a jump, a boundary, or a sharp transition. By examining each direction separately, we can determine whether the function approaches the same value from both sides or behaves differently depending on the direction of approach.