Part 1/6:

Understanding Limits and Asymptotes: A Comprehensive Guide

In the realm of calculus, limits and asymptotes play a critical role in understanding the behavior of functions. This article delves deep into the concepts of vertical and horizontal asymptotes, demonstrating their significance through detailed explanations and illustrative examples.

Defining Vertical Asymptotes

Vertical asymptotes occur in a function when the limit approaches infinity (or negative infinity) as ( x ) approaches a certain value, typically represented as:

[

\lim_{{x \to a}} f(x) = \pm\infty

]