Limits at Infinity and Horizontal Asymptotes

Limits at infinity and horizontal asymptotes are fundamental concepts in calculus that describe the behavior of functions as they approach infinity. When studying the behavior of a function f(x) as x approaches infinity, we are interested in determining whether the function grows without bound, approaches a finite limit, or oscillates. Horizontal asymptotes, on the other hand, are horizontal lines that the graph of a function approaches as x approaches positive or negative infinity. Understanding limits at infinity and horizontal asymptotes is crucial in analyzing the long-term behavior of functions and is essential in various applications of calculus.