Infinite limits

An infinite limit is a limit that increases beyond all values as our variable approaches the limit value. We write it as:

The neighborhood of the point is the open interval around centered in . The open interval is called the (delta) neighborhood of the number . The width of this interval depends on the positive number , which is usually very small.

is a real value lying on the -axis. For an infinite limit, it represents the limit beyond which the functional values of grow as approaches the value of .

The limit is infinite if for any value of that we can find such that when x in - around the point a, i.e. , will be greater than .

Using the limit, we can determine the course of the vertical asymptote in the graph. If so

then the graph of the function has a vertical asymptote in .

Let's have the function . If applicable:

then the following applies equally:

Let's illustrate graphically (the graphs are symmetrical with respect to the abscissa axis):