## Infinite Limits and the Behaviors of Polynomials at the Infinities — A Theoretical Musing

Regardless of your early surrounding or schooling background, we know for one that there are two kinds of *mathematical objects* that are kind of hard to miss in life. The names? **Polynomial** and **Infinity**! While the former might have sounded a bit like the name of a *snake*, polynomials is a *one-of-its-kind* mathematical entity whose perfection defies our mathematical imagination.

For one, polynomials are well-known for being *infinitely smooth* and *never-ending*, while at the same time, they could be a *line*, a *parabola*, or any kind of weird, **infinitely-malleable curve** ready to assume any shape drawn without *lifting* the pencil (kind of). Heck, polynomials are a favorite object of *platonic desire* among math enthusiasts. Talk about the *interaction* between polynomial and infinity!

So with all that goodness, it makes sense for us to inquire a bit as to why despite of having similar forms, the behaviors of polynomials at the infinities differ, leading to some *seemingly-unrelated* insights about their properties in general.

All right. Enough said. Time to buckle the seat belt, and let the theoretical musing begins! 🙂 More