In calculus, a limit is defined as a value that a function approaches as the input values get closer to a certain value. Limits describe how a function behaves near a point, instead of at that point. The limit of a function at a point is the value that the function approaches as the input values get closer and closer to that point. For example, if we start with the function f(x), the limit of f(x) as x approaches a certain value c is normally defined as "the limit of f of x, as x approaches c equals L".

Some key properties of limits include:

• One-sided limits: If a function is defined on an interval and youre trying to find the limit of the function as the value approaches one endpoint of the interval, then the only thing that makes sense is the one-sided limit, since the function isnt defined "on the other side".

• Continuity: Continuity of a graph is loosely defined as the ability to draw a graph without having to lift your pencil. A function is continuous if the limits of the function exist and are equal to the value of the function.

• LHôpitals Rule: LHôpitals Rule is a method of finding limits of indeterminate forms. If the limit results in one of the indeterminate forms, and exits, then LHôpitals Rule can be used to find the limit.

Overall, limits are an important concept in calculus and mathematical analysis, and are used to define integrals, derivatives, and continuity.