#AP Calculus AB/BC: Limits at Infinity & Horizontal Asymptotes 🚀

Hey there, future AP Calculus master! Let's nail down limits at infinity and horizontal asymptotes. This is a crucial topic, and by the end of this guide, you'll be feeling super confident. Let's dive in!

#1.15 Connecting Limits at Infinity and Horizontal Asymptotes

This section is all about how functions behave as x gets super big (or super small). We're talking about what happens way, way out on the graph.

# 🔍 Review: Limits to Infinity

Remember, a limit is what a function's y-value approaches as x approaches a certain value. When we say "x approaches infinity (∞) or negative infinity (-∞)," we're looking at the function's end behavior.

$$\lim_{x \to \infty} f(x)$$ $$\lim_{x \to -\infty} f(x)$$

# 🧐 Finding Limits to Infinity

The key to finding limits at infinity? Horizontal Asymptotes (HAs)! Think of HAs as the "speed limit" for a function's y-values. 🚦

# 🚥 Horizontal Asymptotes

A horizontal asymptote is a y-value that the graph approaches but never actually touches or crosses (at least not at the extreme ends). It's like a finish line the function tries to reach but never quite gets to. 🛑

Image Courtesy of MATH.net

*Caption: The graph shows a function with a horizontal a...