Removable discontinuities occur when there is a hole or gap in the graph of a function, but it can be filled to create continuity. These discontinuities are typically caused by factors like canceled out common factors in rational functions.
Piecewise functions are defined differently on different intervals or sections of their domain. Removable discontinuities may arise when transitioning between those sections.
Limits from Both Sides: When evaluating limits near a point where a function has a removable discontinuity, it's important to consider approaching from both sides to determine if the gap can be filled and create continuity.