Continuity and Differentiability

The category of Continuity and Differentiability explores two fundamental concepts in calculus that are crucial for understanding the behavior of functions. Continuity ensures that a function does not have abrupt changes or gaps, while differentiability extends this idea by measuring how a function changes at a particular point. Together, they form the backbone of mathematical analysis, allowing for the exploration of limits, rates of change, and the shape of graphs. This category will delve into theorems, examples, and applications, providing a comprehensive understanding of how these concepts interact and their significance in various fields of study.