In this section, we will define a limit of a function. We will show how we can use the concept of limit to define the continuity and differentiability of a function.
A limit, in mathematics, is the value that a function or a sequence approaches as the input or index approaches some value.
Continuity, in mathematics, is a rigorous formulation of the intuitive concept of a function that varies with no abrupt breaks or jumps.
A Differentiable function is smooth and does not contain any break, angle, or cusp. That is, the function has a premise it has to be continuous at every point of it. And the function has to satisfy the conditions; no bends, cusps, or vertical tangents. This means that the differentiable functions are very atypical cases among continuous ones.