❖ Finding Horizontal Asymptotes By Using Limits at Infinity - Another Example #1 ❖
📚 Finding Horizontal Asymptotes of Rational Functions Using Limits 🧮
In this video, we work through the process of finding the horizontal asymptote(s), if any, of a given rational function. While you may already know some shortcuts, I guide you through the complete method of determining the horizontal asymptote by using limits as x approaches both positive and negative infinity.
🚀 What you’ll learn:
How to find horizontal asymptotes by dividing every term in the numerator and denominator by the highest power in the denominator.
How to use the result that as x → ∞, 1/x^r = 0 (for r greater than 0) to simplify the function.
The importance of using limits for this approach, which can be applied to any type of function, unlike shortcuts that only work on rational functions.
This is a typical problem you’ll encounter in a Calculus course, and this method provides a solid understanding of how horizontal asymptotes are determined. Plus, I’ll explain the common shortcut of comparing the highest degree in the numerator and denominator and why it's limited to rational functions.
Note: The graph shown in the thumbnail is NOT the graph of the function we are evaluating limits for in the video.
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Watch now to learn how to find horizontal asymptotes step-by-step using limits!
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