Limits at Asymptotes: What's Really Happening [Intermediate] скачать в хорошем качестве

Limits at Asymptotes: What's Really Happening [Intermediate]

In the last video, we learned that limits are about approaching, not arriving. A function doesn’t even need to be defined at a point for a limit to exist. In this lesson, we take that idea one step further. What happens when a function doesn’t approach a number at all, but instead grows without bound? What does it actually mean when a graph “shoots upward” or “falls off the screen”? And how do we describe that behavior precisely using limit notation? Relevant Videos: Limits [Intro] -    • Near vs At: The Limit Concept That Breaks ...   You'll learn: Interpret limits that approach ±∞ Identify and describe vertical asymptotes Distinguish between DNE and undefined Use one-sided limits to analyze asymptotic behavior Estimate limits using algebraic reasoning instead of graphs This lesson is ideal for students in Grade 10–12 math courses including Pre-Calculus, Algebra II, Functions, or Advanced Functions, as well as those studying AP Precalculus, AP Calculus, IB Mathematics (AA SL/HL), IGCSE, or A-Level Math. This can also help those enrolled in post-secondary Calculus courses. Chapters 00:00 - Introduction 00:48 - Building Understanding of Infinite Limits with a Rational Function 1:52 - Important Definitions for Limits 3:19 - Determining Limits from a Pre-Existing Graph 7:49 - Evaluating Limits using Knowledge of Pre-Calculus Functions 9:47 - Sketching a Graph From Limit Properties 13:03 - Recap and Check Your Understanding Question Leave your answer in the comments below, and let us know what kind of math content you want to see next! Like and subscribe for more math tutorials from Your Math X-Plained.