Limits and continuity

The concepts of limits and continuity are typically the starting point of calculus. A limit is the value that a function, or sequence, approaches, given an input approaching some value. The notation is as follows:

This can be read as "the limit of x approaches one of ," and can be solved by just plugging 1 for x to find that the limit is .

Functions can be continuous or discontinuous. When examining the graph of a function, continuity can be described conceptually as the ability to trace the graph without lifting your pencil from the paper.

Explore this section for further detail on continuity, limits, and how their roles in the context of calculus.