Limits at Positive Infinity
So far we have discussed limits at some fixed numbers. In this section we shall be concerned with limits at positive infinity.
Let us consider the function defined by the equation . Let take on the values 0, 1, 2, 3, 4, 5, 10, 100, 1000 etc., allowing to increase without bound. The corresponding function values are given in the table below.




















When the independent variable is increasing without bound through positive values, as in the above table, we say that is approaching positive infinity and write it as .
We see from the given table that the function values get closer and closer to , . Because of this, we say