Subcase of The Big O - Equivalence

You probably have understood what this means just from the title alone. But either way, let's get into it.
Let's take a bit of a complicated example. Consider the following: We want to determine how these functions relate to each-other as x approaches zero. The point is not important here, the behavior is. Don't focus on the zero, it's just what we chose as an example.

If you don't know the basics of trigonometry and the exponentials, please go back and revise. Either way, take a look at the graph.

At any other point, they have totally different values and limits. But as they approach , they both approach the value 1. This is the case of equivalence.

This one's finished.
Whenever you're ready, take a deep breath and start with Landau Notation and Orders of Infinite(simal)s