Infinite limits

In this step we will learn about infinite limits and some of their applications.

• Some functions “take off” in the positive or negative direction (they increase or decrease without bound) near certain values for the independent variable. When this occurs, the function is said to have an infinite limit.
• It is important to understand that when we write statements such as (displaystyle lim_{x to a^{-}}f(x)=+infty) or (displaystyle lim_{x to a^{-}}f(x)=-infty) we are describing the behavior of the function, as we have just defined it. We are not asserting that a limit exists. For the limit of a function (f(x)) to exist at (a), it must approach a real finite number (L) as (x) approaches (a).