👉 Continuity in mathematics is a fundamental principle that connects the concepts of limits and derivatives, asserting that if a function approaches a limit as its input approaches a certain value, then the rate of change of that function at that point (the derivative) must also approach zero or a specific value. In simpler terms, it means that small changes in the input result in small, predictable changes in the output, which is crucial for understanding how functions behave at specific points. This concept bridges the gap between the behavior of functions over intervals and their instantaneous rates of change, forming the basis for calculus and enabling us to analyze and model dynamic systems accurately.
