Final answer:
Limits in calculus pertain to the value a function, sequence, or series approaches as the input or index approaches a certain point. The limit of a derivative is related to the function's changing rate at a point. For time-based continuous processes, none of the limits directly relate to a 'consecutive clock'.
Step-by-step explanation:
The concept of a limit in mathematics refers to the value that a function or a sequence approaches as the input or index approaches some value. Limits are a fundamental part of calculus, which is a branch of mathematics that deals with the limits, derivatives, integrals, and infinite series. When considering the various types of limits, we find that the limit of a function, such as y = 1/x, involves the function approaching a certain value (asymptote) as the input grows closer to a specific point — in this case, as x approaches zero, y approaches infinity, indicating that the function has a vertical asymptote at x=0. On the other hand, the limit of a sequence pertains to the value a sequence approaches as its index (usually denoted as n) goes towards infinity. A limit of a series would be the sum of the terms of a sequence, which may converge to a specific value as the number of terms grows infinitely large. Lastly, the limit of a derivative can be thought of as the instant rate at which a function is changing at a particular point and is related to the concept of a function's slope at that point.