Limits At Infinity, Part II :  In this section we desire to take a look at some other kinds of functions that frequently show up in limits at infinity.  The functions we'll be discussed at here are natural logarithms, exponentials,  and inverse tangents.

Let's begin by taking a look at some of very basic examples involving exponential functions.

Example:  Evaluate following limits.

Solution

The major point of this example was to point out that if the exponent of an exponential goes towards infinity in the limit then the exponential function will also go towards infinity in the limit.  Similarly, if the exponent goes to minus infinity in the limit then the exponential will go to zero in the limit.