a limit is the value that a function approaches some value. In formulas, a limit is usually written as

and is read as “the limit of f of x as x approaches a equals L”.

Rules for Limits:

(baengballs.de)

Continuity:

A function is said to be continuous over a range if it’s graph is a single unbroken curve. A function f(x) is said to be continuous at a point X0 if

Differentiability:

A function is said to be differentiable if the derivative of the function exists at all points of its domain. If a function is differentiable at a point, then it is also continuous at that point. A function f(x) is said to be differentiable at a point x = c if f'(c) is existed.