How is Continuity Related to Limits in Calculus?

In calculus, the concepts of continuity and limits are closely connected. Continuity refers to a function's behavior at a particular point, while limits describe a function's behavior as it approaches a certain value. In mathematical terms, a function is continuous at a point if the limit of the function as it approaches that point exists and is equal to the function's value at that point. This relationship is fundamental in calculus as it allows us to understand how functions behave in specific points and as they approach certain values.